We go camping with our daughters each summer (usually in New Hampshire), and I can't even tell you how much they love it. . . How about a national park? Or a family-style resort on a lake or in the mountains?
Otherwise, for warm and sunny, there are all of the family resorts in the islands -- Beaches is one, but there's one called JFK something or other in Jamaica that is more affordable and looks neat. There are others, too, but I just don't know them off the top of my head . . .
Pretty soon, though, I'd say when our youngest is 4, we plan to resume more "exotic" travel. We LOVE to travel, and I look forward to going abroad with our girls. Of the trips we've taken (without kids), I'd feel comfortable bringing my kids age 4+ to just about anywhere. I think they'd love Costa Rica ("tame" volcanoes, beautiful beaches, great wildlife viewing, rain forests), Africa (we saw TONS of families with YOUNG kids -- even babies -- when we visited Tanzania)(great wildlife viewing, beautiful beaches), Thailand (wildlife, forests, beaches, culture, great city life, they love children), and even Europe -- though I'd do a more nature-oriented trip with kids, preferably, unless I had a lot of time to take the culture slowly. . .