A modern pavilion built near the center of the old palace complex.
Ayutthaya's grand royal palace once occupied around a fourth of the island, north of the Si Sanphet temple. The palace buildings were built mostly of wood, so they were completely leveled when the Burmese sacked and burned the city in the eighteenth century. Brick structures were in turn torn down and shipped down the river to build the new capital at Bangkok.
When Ayutthaya was founded in the mid-fourteenth century the royal palace was originally located in the area near Wat Phra Ram that is now a park (or, possibly where Wat Si Sanphet is today - accounts vary). It was moved north to the area between Wat Si Sanphet and the river in the mid-fifteenth century.
Since the palace was completely leveled by the Burmese invaders, there's nothing really to see and in fact there is little of the way of formal paths or signs in the area. An open-air Thai-styled pavilion was built in the middle of the area a few years ago, but it's not open to the public. The area can make for a pleasant late afternoon walk, but there really just isn't anything to see. You have to use your imagination.
In theory, admission to the palace is included in the admission to Wat Si Sanphet, but it's easy to gain access to the grounds from any of the circling roads.