Been doing some research myself and you can get a water taxi from the marine terminal (5 min walk from ship) to either Caye Caulker or San Pedro. Round trip price is $17.50US. Check www.cayecaulkerwatertaxi.com for time schedules and other destinations.
isle-------in Belize, your ship will "dock" in the middle of the sea....the tender to Belize City will take you about 40 minutes (ask first, to be sure). Anyway, if you arrange a tour through the ship, you'll probably be picked up and dropped off right at the ship, saving time (again, ask for details). If you want to do it on your own, like DebG said above, there are water taxis once you tender into Belize City. There are no beaches near the port......the water taxis wil take you to little islands called cayes. In any case, do your research before you get there and don't miss the ship! We usually do our own excursions, but, in Belize, felt more comfortable on a ship sponsored tour.
I would take the ship sponsered trip to Goff's Caye.
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We just returned from a cruise including a Belize stop with our boys ages 4 & 2. We took a water taxi to Caye Caulker. While the Caye was very beautiful it was not worth the 45 minute one way trip on a very crowded and rough water taxi (I also never saw a life jacket on the boat). We call it our adventure. By the time we took the tender to Belize City and then the Water taxi to the caye we had only about an hour and a half to play before the 45 minute return trip. Even the beaches there are not great - lots of exposed concrete and rebar. We ended up exploring the island mostly. I would recommend taking a ship sponsored excursion after seeing the "real Belize." It is fine for adults but a little wild for kids.