Depending on whether you want to stay in/near town or in a lodge outside of town, among the places I'd recommend you check out are:
Aguada -- best bargain in Cayo at US$25 for a/c room. There's a pool, restaurant and new rooms upstairs.
Martha's -- good locally owned hotel, with restaurant (and laundry).
Log Cab-Inns -- nice Belizean owned place, with pool and individual cabins.
Clarissa Falls -- on the Mopan River, friendly, good little restaurant
Crystal Paradise -- I agree with Katie on this one
duPlooy's -- they have moderate/budget rooms in addition to more upscale digs
Chaa Creek camp -- US$50 per person including excellent meals, in their "safari" camp, little units on raised platforms
Prices will be lower than in-season, but the breaks aren't as much in general as at the beach hotels.
There are many tours to Tikal -- several large operators (Windy Hills, Chaa Creek, Maya Mountain, others) plus independents, some of whom you can reach at Eva's restaurant. You can also take a bus or minibus from the Guate side.
There have been some incidents at Tikal recently -- a reported rape and killing -- and there is supposed to be increased security at the park. Check locally when you get there to see what the latest situation is.
Belize First Magazine http://www.belizefirst.com/