The ruins of Vijayanagara cover 26 square kilometres — too large to walk in a single day. The main options are bicycle (rentable from several shops in Hampi Bazaar for around Rs 100–150 per day), auto-rickshaw (negotiate a price for a full-day tour, typically Rs 400–600), and moped (available for rent if you are comfortable riding one on unpaved paths).
Cycling is the most rewarding way to see the site: the riverside path from the bazaar to the Vittala Temple is flat and shaded, and you can stop at will. The royal enclosure cluster (Lotus Mahal, Elephant Stables, Queen's Bath) is about 2 km south of the bazaar and easily reached by bicycle. Note that the path to the Vittala Temple passes through a stretch of deep sand where bicycles must be pushed — allow extra time.
Auto-rickshaws are the practical choice for the heat of midday, or if you are combining several distant clusters in a single day. Most drivers know the site well and will suggest a logical route. Agree on a fixed price before departure.