First decide how do you want to do it: walk, bicycle, moped, auto-rickshaw, car. There is even a buggy service available for a limited stretch. And then there is a tonga (horse cart) option too. Keep in mind entry of motor vehicles is restricted at many sites in Hampi.
The auto-rickshaw & car options are faster, but leaves out the thrill of you 'exploring' the sites.
A very popular strategy is to hire a bicycle or moped(if you have less energy/time!) to cover the distances and do it on foot.
For the sake of explenation here, we've divided the area into 5 clusters, each needs about 4 hours to explore. Also 5 tentative routes are suggested. The clusters and the routes are marked on the Itinerary map. Depending on your situation, you may need to customize your plan, than say follow it verbatim as detailed here....
Route 1: Covers the Sacred Center surrounding the Virupaksha Temple vicinity. Start from the Sasivekalu Ganesha pavilion on the slops of the Hemakuta Hill facing the main road. This is on the south end of the hill.
Climb up further (it's a gentle slope) to explore the Hemakuta Hill Shrines in a south to north direction. (there are many temples and gateways to see here).
After Virupaksha Temple visit take the Hampi Bazaar and come towards the Hampi Bus stand area. Head further south on the main road. The Kadalekalu Ganesha and Sasivekalu Ganesha shrines appears on your left, by the slops of the Hemakuta Hill.
Now you are back to the point where begin this walk. You may pick up your bicycle/moped parked before venturing on to Hemakuta Hill, and head for the Krishna Temple and the Krishna Bazaar located southward. After this head further south till you spot the signboard for the Lakshmi Narasimha Temple and the adjacent Badavilinga shrine. Take a detour by walk (bikes/mopeds not allowed). Back to the main road. Head further south. The road makes a bend around the Chandikesvara Temple and the living Uddana Veerabhadra Temple. You'll also spot a tall monolithic lamp-post by the corer of the Chandikeshava Temple and a sati stone (memorial of wife who burned herself in the pyre of her dead husband) beneath it. So this is the culmination of your sacred center lap.
You can now head for the cluster 3, that is the Royal Center cluster. This itinerary starts at Sisters Stones, which is about 500 meters/0.3 mile south.
You may even do the Route 1 in reverse direction, that is start from Chandikeshava Temple and end at the Hampi Bazaar/Virupaksha Temple locality.In this case you can proceed for the Route 2 or Route 5
This is a 3 km/2 miles walk, rather trek, from the Hampi Bazaar area to the vicinity of the Vittala Temple. You'll essentially covering the Riverside Ruins and large deal of monuments, boulder formations and of course the river Tungabadra's gorge. No motor-able trails. At the best you can carry your bicycle, if you are prepared to carry it about half the route which is boulder strewn trails.
After Hampi Bazaar exploration head to the far end of the street where you'll find the Monolithic Bull pavilion.
Right next to it is a flight of steps to a small hilltop where you'll find a tiny Hanuman shrine with a beautiful image of Hanuman in the boulder inside the shrine. As you descend, you'll be in the vicinity of Achyuta Raya’s Temple.
After the Achyuta Rayas Temple visit take the wide street in front of it with ruined pavilions on either sides. This is the Courtesans Street. Midway on this ancient street you'll find a restored temple pond called Pushkarani.
Towards the end of the street on your right is the Rangatha Temple with a large image of Lord Vishnu in reclining posture with his consorts sitting by his feet. Nearby is the Varaha Temple with a incomplete gateway where you'll find the Vijayanagara Emblem engraved on it's gateway.
Take left after you exit the Courtesan’s Street. You'll find a few living temples and shrines here. Visit the Kodandarama Temple facing the river, Yantrodhara Anjaneya Temple a little up and behind Kodandarama Temple and of course the Chakratirtha where the river make a sprawling expanse before plunge through a narrow gorge. You'll also find people offering coracle crossing or short coracle tour (recommended) around this area.
Trace the riverbank eastward from here, you'll discover some interesting carvings and shrines, like a 1008 and 108 siva linga carved on a sheet of rock, a beautiful image of Parvati, avatars of Vishnu etc. No marked trails. You need to scramble over the massive heaps of boulders to explore the Riverside Ruins area. Leave the bicycle back somewhere near the Kodandarama Temple or Varaha Temple to be picked up after you've explored this boulder strewn stretch of your itinerary.
You'll see the pyramid shaped tower of the Narasimha Temple up on the gentle slops overlooking the river. Nearby is the Sugreevas Cave with ocher and white stripes painted on the boulder. From the vantage points of Narasimha Temple you can also get a fine wiew of the rest of the trail ahead, including the remains of an Ancient Bridge across the river. The trail now passes through a two storied gateway and ends in the vicinity of Vittala Temple. Before that you'll find a tall archway like structure popularly called the Kings Balance made of slender boulder pillars. At the base of the King's Balance you can find the image of Krishnadevraya, the most well known kings of the empire. Other attractions around the Vittala Temple are the Inscribed Vishnu Temple and the Purandradasa Mantapa by the riverside.
Like mentioned in case of Route 1 , you may do Route 2 also in the reverse direction, that is start from the Vittala Temple and end at Hampi Bazaar. Reserve some 3-4 hours for this route.
This is a 3 km/2 miles or so trail where you'll explore the core of Hampi's citadel. This area is called the Royal Center as most of the imperial complexes of the erstwhile capital is located. You can take bicycle/moped to most of the monuments in this trail. Some level of walk is indeed needed.
Start from the Hampi main road at the Sister Stones , locally called Akka Tangi Gudda .
This is a natural archway formed by two giant boulders one leaning on the other. It's partly collapsed recently due to a fissure one one of the boulders.
A little south, leave the main road and take the dirt track. You'll see signposts for Royal Enclosure at the junction.
The next stop is the Underground Siva Temple a temple complex located beneath the ground level.
A little ahead you'll pass Noblemens Quarters which is sprawling residence complexes , only the foundations remain. The nobles of the Vijayanagara court lived here.
Further ahead enter the walled complex called the Dannayaka Enclosure where you'll find a maze of walls and basement of erstwhile palaces. Not everything is marked with signposts.
At the corner of this enclosure is a massive watchtower called Mohammadan Watch Tower with dome roof, a fine example of Vijayanagara military architecture.
Deep inside this area explore the Band Tower, The Mosque , the Mint area , Palace of Vira Harihara , Palace of Krishnadevaraya , a number of ponds, a platform to alight from elephant etc.
Exit this enclosure and continue on the mud track that will join another trail near the Hazara Rama Temple , which is one of the main attractions in this area.
Facing Hazara Rama Temple is an ancient street curiously called Pan Supari Bazaar (beetle-nut market) with a number of pavilions and other ruined structures.
Near to Hazara Rama Temple is the entry to the Royal Enclosure , the citadel. Right next to the entry point look for the Large Stone Trough used to hold water for the horses of the nobles attending the court.
There numerous attractions inside the Royal Enclosure like the geometrically thrilling stepped tank , the underground chamber which served as the war room for secret discussions , massive aquatic complexes, the king's audience hall and the tallest structure the Mahanavami Dibba from which the king watched the military parade .
Come out of Royal enclosure, you'll find two massive Stone Doors kept near a tree.
Heading north will take you to another enclosed area called Zenena Enclosure (the harem) and behind it the Elephant Stable and the Ranga Temple all must visit attractions. You may plan to visit Zenena Enclosure on the same day you've visit the Vittala Temple as the tickets are valid for the same if used on the same day. (So these two monuments are included in Route 4 itinerary )
From the Stone Doors if you head south, the mud track finally joins the Hampi main road. At the junction is the Queens Bath used as pleasure pavilion by the royal households.
After Queen's Bath take the main road and head towards Kamalapura direction. You'll find a signboard for the Chandrashekara Temple and the Octogonal Bath . From Chandrashekara Temple a trail goes towards the Saraswathi Temple (Saraswathi Temple 2) on a small hiltop. Further ahead on this trail is the Octogonal Bath and a number of palace complexes . Only the basement of the palaces remain, the Octogonal Bath is worth visiting.
If you scramble through the cowherds trails in this otherwise featureless plains , you can reach the Srinagarada Hebbagailu which was a massive gateway to the citadel on the Pan Supari Bazaar mentioned earlier.
The route starts with Zenena Enclosure in Royal Center and ends with Vittala Temple complex. By far this is the longest route (about 10km/6miles).
The reason for clubbing these two monuments in one itinerary is to save some ticket cost (Rs 10 for Indians and nationals of SAARC and BIMSTEC countries ; others pay $5) . The ticket is valid for both Zenena Enclosure and Vittala Temple , if used on the same day. Otherwise , you can club Zenena Enclosure with Route 3 and Vittala Temple with Route 2 , and manage the rest of attractions in Route 4 and separate short detours.
Anyways let's start with Zenena Enclosure are where the ticket counter is located. After Zenena, visit the Elephant Stable (a must visit) and the guard's quarters nearby. Behind this (a roundabout path) is the Ranga Temple with a massive image of Hanuman.
Get back to the main road and head to the Kamalapura town square. You'll find the Archeological Museum here. A large replica of the Hampi's site is a valuable attraction here alson with display of many Vijayanagara artifacts. They also sells a very compact Guide Book on Hampi.
A scoop! If you are keen on a hidden gem of Hampi, head to the Pattabhirama Temple from the museum , its further half km from the museum on the same road. Go along the fringes of the village, after about half km, appears a left diversion. On this diversion you'll see a canal and a bridge shortly. Pattabhirama Temple's entry is just a few meters from here.
Back to Kamalapura main road. Head towards Kampili on the main road. In 1km you'll spot Ganigitti Temple on your right by the side of the main road. A little off from this point is the Bhimas Gateway with some beautiful mythical themes carved on the wall.
Back to the main road, another 1km towards Kampili, appears a Y fork. The left goes to Vittala Temple. Otherwise continue straight on the main road for Malyavanta Hill a recommended place to visit. About half km from the Y fork you'll see the archway to the hilltop Malayavanta Raghunatha Temple which is a living temple. There are many things to see here esp. the carvings on the boulder, temple architecture in which massive boulders in its natural position is merged into the rest of the temple complex. A cave shrine under a boulder and so on. The view of the valley from here is fabulous. The plus is , you can take your moped/car all the way to the hilltop, through it is a stiff climb.
Back to the Y fork to Vittala Temple. You'll pass numerous monument structures, some unnamed and a few major ones before reaching the Vittala Temple. Ahmed Khan’s Mosque and Tomb appears on your left and you'll pass through Talarigatta Gate. After Gejjala Mantapa take left for Vittala Temple or continue straight for the coracle ferry point.
A wide pavilion lined street called Vittala Bazaar leads to Vittala Temple. Somewhere midway on the Vittala Bazaar are Kudure Gombe Mantapa and temple pond called Pushkarani which was the venue for the boat festival. You'll need over an hour at least to visit Vittala Temple complex.
So this is the end point for Route 4. Further you may take the Route 2 to Hampi Bazaar area. Or take the coracle ferry (mentioned just above) which is your gateway point to Anegondi area exploration. This is explained as Route 5.
Before we jump into the one day Hampi itinerary, let's understand a few things. The attractions in Hampi is spread around a very large area (25sq km). Accessing these these involve a good deal of walk (trek), cross the river in a coracle, ride a moped or even hire a local taxi (auto rickshaw). Even in the best scenario, you would have walked almost 3-5 hours of the day.