Ayutthaya is not a big food city, which is not to say that you won't have plenty of dining options to choose from. It's just that in many visits there I haven't found anything really 'special' to mention. There are a number of restaurants catering to travelers on the street facing Wat Mahathat. These are good options for lunch, so it's good to plan your day to be at Wat Mahathat or Wat Ratchaburana around noon as there are few other dining options within the historical park.
You'll find another collection of restaurants with varying menus along 'Farang Street' near the main fresh market. Along the various river-fronts there are also a lot of restaurants, especially around the southern tip of the island near Pom Phet fort. These are generally seafood restaurants, as incongruous as that may seem. Ayutthaya actually is famous for giant river prawns, but I didn't see them on offer in many places the last time I was there.
The adventurous will find a good selection of street food in various locations around town. The big local delicacy is something called roti sai mai, an incredibly sweet dessert that looks like fine pastel colored pasta and tastes like cotton candy. It's typically eaten rolled up in a thin rice flour pancake. The streets around Ayutthaya Hospital in the south-central part of the island are lined with stalls selling the snack in big plastic bags.
There seems to be very little in the way of nightlife in Ayutthaya. You will find beer and local spirits on sale in most restaurants, and several of the guesthouse restaurants seem to have some live music at least some nights, but on the whole Ayutthaya is a very quiet place.