We enjoyed Belize, but you should do a LOT of research. It is not easy to get around the country on land unless you rent your own van (we did) or like unairconditioned buses (we don't), and the short plane trips on Mayan Air and Tropic Air, while convenient, are not cheap.
We visited Tikal prior to Belize; it's a good spot if you're into Mayan ruins. The Tikal Inn is in the park which is convenient since you'll need about an hour drive from the hotels that are not in the park. The downsides to the Tikal Inn are that (1) it is not air conditioned (really, not a problem until 10pm when the ceiling fan goes off (see next), and (2) electricity only runs from 6-8am and about 6-10pm; it can be "exciting" trying to dress and pack in the dark for a sunrise ruin tour at 5:30am!
The zip lines through the trees (canopy tour) outside of Tikal were good.
The drive from Tikal to San Ignacio, Belize is a bit rugged, since the last fifteen miles or so in Guatemala are dirt road. I did not like the house that we rented in San Ignacio (Kumquat Cottage -- the name should have been a giveaway!) because the ventilation was just awful -- no breezes at all through the windows; it did have a/c in the bedroom, and that made it tolerable.
As mentioned, one cave tour out of San Ignacio is the ATM (Actun Tunichil Muknal). It's an interesting trip, involving a one hour drive from San Ignacio (the last 30 minutes on dirt road), a 45 minute jungle hike with three river crossings (not a bad walk, really), and 2+ hours swimming and wading through water, climbing over, under and around boulders and up one very tall ladder to get to the "Crystal Maiden". Maybe I'm just old (Hell, I AM old!), but I'd recommend that anyone on this trip be in decent shape, and not too obese. All those caveats aside, we were the only two people in the cave when we visited, and that was pretty neat.
Mayawalk Tours in San Ignacio can arrange cave and ruin tours in Belize and, I believe, for Tikal. I thought that the people there were very nice.
In short, there are a lot of things to do as well as dive, but I wouldn't try to do too much in a short time