The large area means you probably need the whole to walk, or cycling (bike rental is available), around to visit the legendary architectures to learn the history of Ayutthaya.
Highlights include Wat Phra Si Sanphet, Wat Mongkhon Bophit, Wat Na Phra Meru, Wat Thammikarat, Wat Ratburana and Wat Phra Mahathat temples, all of which can be easily visited on foot. In the south of Wat Phra Si San Phet finds Viharn Phra Mongkol Bophit where Thailand’s largest bronze buddha image is enshrined.