Nakorn Si Thammarat is well know for its food, and the fact that its off the tourist trail means it's also one of the cheapest places to eat you'll find. As with everywhere else in Thailand, there's no end of options for street food where-ever you go. The night market near the train station is the best place to go for a street food dinner.
For more traditional restaurants, the Bovorn Bazaar has the most choices in one place. Hao Coffee is a small coffee shop with an extensive food menu that makes it a good choice for breakfast or dinner. Glass topped tables are filled with old watches, lighters or other collectibles, making every meal interesting. In the center of the courtyard is Krua Nakorn, offering Thai curries on rice in a street food style where you select what you want from the pots of already prepared daily specials. At the entrance to the bazaar is a small bakery where you can also get breakfast.
On Pak Nakorn road, the A&A Bakery offers great cakes and good food as well. Further down the road is the Nakorn Garden Inn with its restaurant housed in a charming old house.
If you've a hankering Italian food, all is not lost. Visit Italy Pizza out next to the Twin Lotus Hotel.
For drinks, it's back to Bovorn Bazaar and 99% Rock.