I agree about Belize City.
We stayed on Ambergris Caye, in a house that was in the relative boonies, so not super convenient-but-not-really-inconvenient, although it was stunning, and happened to be next door to a fantastic dive op (White Sands). Many of the DMs there were aspiring cave divers and were quite excited about my gear. Most dive sites are minutes from anywhere on the east side of the island.
Our non-divers in the group were able to book several tours of the ruins and to the zoo on the mainland,with pickups on the dock out front, and there were plenty of fishing ops in the area, although we didn't hire them. The town of San Pedro can admittedly be lovely or cheesy, depending on where you go. We had great fun exploring the rest of the island in our golf carts, but you don't necessarily have to have one.
On our last day us divers went to Lamanai, which are fantastic Mayan ruins and involved a pretty awesome boat ride up a river to get there.
But other than the river ride to Lamanai, I HIGHLY recommend traveling by puddle jumper over boats if you are staying on one of the cayes and traveling. The ferries are long, sometimes really hot rides, unless you splurge for a super fancy one, and then you might as well take a 15 minute plane ride for the price. And while the ferry vs. plane price is pretty dramatically different for getting to and from the islands initially, it's not that different if you're doing a tour.
We opted not to do a Blue Hole trip. It's an all day trip, most of it traveling, and I've heard mixed reviews. If it's a dream of yours, yay! Go and enjoy.
I'm a die hard IPA girl, but I adore Belikin beer. And if someone offers you conch fritters, try them! And don't be afraid of the habanero/onion relish that pops up in the cuisine, it tastes like burning, but delicious burning.
I haven't been to Turneffe Atoll but have heard great things. I doubt you'll go wrong. Most of the above would still apply.
Come to the nerd side, we have pi!