Belize is indeed a tender port--about a 12-15 minute ride on a pretty high speed tender.They have a variety of tenders-- seems like no two are the same but expect about 12-15 minutes to the dock from the ship.
Regarding what to do, as you have not said what you're interested in doing that would be hard to offer up much advice.
There's a tourist village at the dock with some pretty good shops--pretty clean, etc. one or two restaurant/ bars--Wet Lizard is one that comes to mind. Out behind the tourist village you'll find some stalls, shacks, etc. where the local folks sell a variety of tourist thingees. I would not wonder too far from the tourist village on my own if I were you.
If you're into Mayan Ruins, there's a few tours --one is a tour to Altan-Ha, includes a ride on the river, bus ride to the ruins, etc. and allows time then for shopping around the dock area. There's tours to outlying islands and snorkeling. I would suggest that since you apparently haven't been to Belize, that you browse the ships tours and pick one that interests you through the ship.