I don't think scorpions are as common in San Pedro town as they are parts of in mainland Belize, though I personally have seen a few of them in San Pedro. I've even seen kids "playing" with one, on the street that goes up to the hand ferry.
So far as I know, scorpions in Belize are not a species that has a fatal or really serious sting. I've seen young kids of five or six stung by them and their moms treated it as they would a bad bee sting.
They seem to like damp, dark places such as in walls and under rocks. Don't leave wet towels out overnight, as sometimes they will get under the towel.