Keep an eye out at Flea Market — you're likely to discover some unique curio among the stalls here. After you've found the perfect souvenir, try some fare from one of the nearby food vendors.
You'll have no end of sightseeing choices when visiting Nuku'alofa. Flea Market is a good place to start here, but there are many other fine spots to discover. Royal Palace of Tonga, Ancient Tonga, and Tongan National Centre are not far from the community marketplace and will fill in your day nicely.