If you're interested in taking a local tour, check well ahead, since they need a certain number of people to run a tour and don't go every day.
Friends Tourist Center, next to Friends Café on Taufa'ahau Road, books several different island tours, activities, and accommodations. They arrange transport to traditional Tongan dance shows several times a week.
Teta Tours, at Railway and Wellington roads, also offers sightseeing tours. The Tonga Visitors Bureau and most hotels can also help arrange sightseeing tours. Few of the road tours operate on Sunday and it's more common to do a boat trip to one of the islands off Nuku'alofa that day.
Mana Kelepi's "Something to Do on Sunday" tour at 0930 includes a church service, visits to Christian sites, and a family umu feast. You must book by Saturday at Friends Tourist Centre.