There are lots of options for places you can snorkel from shore in Belize but, unfortunately, most of them are really expensive. Tobacco Caye will likely be your lowest cost option for decent shore snorkeling. Nearby South Water Caye is excellent but spendy, as are most of the options on the outer atolls. The reef is out +/-20 miles so you can't snorkel from the mainland. Glover's Atoll Resort (45-50 miles out) is a budget place that has world class shore snorkeling, but it requires a full week (out Sunday and back Saturday) unless you want to pay $350US for a ride in or out midweek.
The reef on Caye Caulker isn't as healthy as the outer atolls because it gets more pressure but the snorkeling is still pretty amazing - sharks, rays, schools of tarpons, big jacks, moray eels, turtles, even manatees sometimes. You can snorkel a bit at the cut (a channel through the island) if you're easily impressed. It will likely cost $20 or more for a snorkeling trip; we paid $45 each for a full day snorkeling/sailing trip with Raggamuffin last summer and it was worth every dime - really amazing. I love the vibe on Caulker - some great places to eat and stay in a variety of price options and we met and spent time with some friendly, interesting locals which made our stay more memorable. If you really only have 3-4 days for the blue water part, Caulker would mean less travel time and more time kicking back or exploring than the more southerly cayes, too.
I've only visited Belize twice but it's been for 3-4 weeks each time; check out the link below and let me know if I can answer questions. Happy trails!