In Belize, you have to tender into the actual city. This means, they use smaller boats to take you from your ship to the shore. Belize would actually be a place I'd do an excursion, either through the ship or through shoretrips. The snorkeling there is fantastic. In Costa Maya, you can grab a cab to go downtown, actually it's to the actual city which is a quaint little fishing village. We went to the Tropicante and had a great time. We were able to get a table and chairs, they also had loune chairs available. They had great service, you never went hungry or thirsty, and they ran a tab for us. The restaurant/bar itself is across from the beach, but the chairs are right on the beach. It's a great way to spend the day, good snorkeling, too.
Hope you have a marvelous time!