I would say, first, that Ambergris Caye, nice as it is, is just the tip of the iceberg, or cocoberg or whatever, of Belize. Ambergris is a mid-sized island about half the size of Barbados, whereas Belize is a country the size of Massachusetts with a surprising diversity of environments -- besides some 200 islands in the Caribbean there are rainforests, mountains, whitewater rivers, huge cave systems, not to mention Maya ruins, 500 species of birds, 700 or 800 kinds of butterflies, jaguars and all kinds of wildlife.
Ambergris Caye has many good restaurants, but so does Belize City, Placencia, Caye Caulker and some other spots in Belize.
But, yes, Belize is in the Western Caribbean and for the Western Caribbean the peak hurricane season is late August through early November. Keith hit Ambegris Caye in late September last year. Having said that, though, hurricanes are relatively rare in Belize, with one serious one about once every 10 years, and the last really bad one before Keith was in 1961. You are much more likely to be in a hurricane in Texas, Florida or in the Southeast US than in Belize.
Most travel agents know only a few places in Belize, if any at all, among them always Ramon's. You might look around this and the other Web sites on Belize for more information on the huge variety of places available, from luxury condotels to villas to cottage colonies to cabanas on the beach to jungle lodges.
Belize First Magazine http://www.turq.com/belizefirst/