I've been to both the Caribbean and out west, both make excellent family vacation spots. If you go Caribbean, I wouldn't go to an all inclusive resort as that would tie you down to one spot and, as much fun as playing on a beach in a beautiful locale can be, it wears thin after a few days. I would suggest a cruise. There is no better vacation with kids (well, maybe Disney). They have excellent children's programs, good food, and you'll be able to enjoy a variety of fascinating locations.
However, all that being said, I'm going to put a vote in for going out west. I took a 17 day road trip with my husband this last fall and it was amazing. The variety of things you can see, and expose your kids to, is pretty much unbelievable. You could spend a month in Utah alone!
Our trip included: the Badlands, Mt. Rushmore, Wind Cave, Crazy Horse, Jewel Cave, Devils Tower, the Bighorn Mountains, Bighorn Canyon (a little out of the way spot that really is not to be missed), 3 days in Yellowstone, the Grand Tetons, Grand Staircase Escalante, Capitol Reef, Bryce, Zion, a number of Utah state parks (which are seriously cool, by the way, Utah knows how to do state parks), the Grand Canyon, Antelope Canyon, and Mesa Verde. We didn't get to do everything on our list either, we have to go back for Arches and the whole Moab area.
You can get an America the Beautiful pass and that gets you entrance to all the national parks. It lasts a full year and we'll be using ours again this spring when we go to Kentucky. Your budget would allow for you to stay in local hotels, but alternatively you could think about renting an RV and "camping" to a certain extent.
Here's the website of a road tripping family that we read for inspiration when planning our own adventure:
http://www.cross-country-trips.com/