Of course, since you only have one day there is no possible way you will get to experience all of the wonders Belize has to offer. My suggestion is that you concentrate on one site and enjoy it to the fullest. One possibility is Ambergris Caye where you can kayak, snorkel or just enjoy the scenery. Another possibility is to enjoy a day in Belize City. It has more to offer than meets the eye, and you can enjoy the markets, crafts, restaurants and shopping.
Hope you have a great trip.