Friend's Cafe
The main place for tourists on Tongatapu. Serves coffee, tea, and excellent breakfast. Try the vanilla french toast. The milk shakes are also very good. There is an adjacent souvenir shop, information desk, and computers for internet access
For a small town, Nuku'alofa offers a decent range of restaurants and bars. Expect to pay 15-40 Pa'anga for a main course in a restaurant and about 5 Pa'anga for a takeaway at one of the roadside sellers. Seafood is usually good.
The Oholei Beach Dinner and Show is set in Hina cave on the beach on the south-east side of Tongatapu, near the airport. It includes a Tongan dinner and a traditional show inside a limestone cave. The cost is about T$30 each and can be booked from the Tonga Visitors Center. Transport is extra. Make sure you understant the travel arrangements when you make the booking e.g. where and when to be picked up.
Most restaurants and eateries are closed on Sunday but there are a couple of Chinese restaurants which are open Sunday.