Keep in mind, first, that Ambergris Caye is not all there is to Belize. It's just one island out of several hundred, albeit the largest. And then there's the mainland, about the size of the state of Massachusetts.
Ambergris Caye definitely is not centered around diving. Twenty years ago, most visitors to Belize and to Ambergris Caye were divers. Now a majority, including visitors to Ambergris Caye, do not dive.
Due to the barrier reef just offshore, the beaches inside the reef do tend to have shallow water and seagrass. However, you can swim off many beaches including many areas on Ambergris Caye. Hotels usually remove seagrass from an area at their piers to make for better swimming. The Caribbean is usually warm and clear and makes for pretty good sea swimming. Many hotels, especially on Ambergris Caye, also have pools.
Belize books and publications by Lan Sluder:
Belize First Magazine (http://www.belizefirst.com
Fodor's Belize & Guatemala Guide (new 4th edition coming this summer)
Adapter Kit: Belize (the first and only comprehensive guide to living, retiring, working and investing in Belize -- a best-seller on Amazon.com)
San Pedro Cool (the first and only visitor guide to Ambergris Caye)
Belize First Guide to Mainland Belize
UpClose Central America
Belize Book of Lists