Good suggestions on mainland activities.
A couple of thoughts: Belize City isn't a tourist town and is certainly not for the faint of heart, but there are some interesting things to see and do there. Just make sure you're doing them in broad daylight with lots of people around and don't wander off the main streets. There's the Swinging Bridge, the Governor's Mansion from the British Colonial days, St Johns Cathedral if you can get inside, the old American Consulate (especially interesting if you ever read
Our Man In Belize), the former prison now turned into a museum, and just the general vibe you get from wandering around a "city" in a Third World Country. The walk along the sea wall is fun, too. You can stay at the Ft George Radisson, which is where the liveaboards dock or more appealing to me is The Great House right across the street. There's also Villa Boscardi, which is on the way to the airport and not nearly as fancy as it sounds. The walk along the sea wall is interesting, too.
Don't bother with "Tourism Village," which is where the cruise ship visitors are herded through on their way to Cave Tubing, etc.
A trip to Tikal would be tight on a two-day stay on either side of your stay.
If you choose to go to Placencia, my destination of choice, you'll probably have to fly. It's only a thirty minute flight but still you're going to spend a half day traveling. There are tons of mainland stuff to do there as noted above plus hiking in the Cockscomb Basin, the first Jaguar Preserve. You can dive Glovers from there with Splash. It's a long trip, maybe three hours?, but well worth it imho. But really I don't see how you can make it work given the time constraints and of course you don't want to violate the No Fly Rule.
Here are some random shots I took in BZ City.
Edit: Thinking about it some more, I suggest you focus on things that are an easy jump from Belize City, like Lamanai, cave tubing, zip lining (gulp) or consider traveling to Placencia or San Pedro in the evening--but not darkness-- to give yourself a good jump on the next day. You'll have time to do everything but relax, lol.
