I'm trying to find somewhere cheap and cheerful to go with my family for a week in August. We are two adults and two boys, 10 and 12. We're looking for the perfect combination of beautiful beach with great snorkeling and water sports and a small town nearby that we can explore. We don't want to be tied to taking guided tours or feeling unsafe if we leave the hotel property. Getting around by boat or kayak would be great. For accommodations, we'd like a small hotel, low-rise or bungalows or a condo. Nothing fancy, clean and basic are fine but a pool and hot tub are important as is beachfront location.
For food ideally I would like to have a fridge or kitchenette so we can eat some meals in the room and go out for others but I'm not closed to the idea of an all-inclusive.
We've only been on one other vacation to Ambergris Caye in Belize and it was perfect except the hassle of getting there.
The out islands of the Bahamas have caught my eye but I don't know if any of them fit the bill. Any suggestions will be greatly appreciated. Thanks very much.

I hadn't considered it. I'll look into it. I'd heard that D.R. is not the safest when you leave the resort properties. Is that just bad information I got? Thanks.

I would only consider the DR if you truly want an AI resort and organized off property tours, which you stated you really didn't want, so I feel that response has a hidden agenda in it.

Look at St. John, USVI. It has a lot of what you said you are looking for and easier to get to from the US.

The Club Med Columbus Isle in the Bahamas looks good. I'm not sure if it's adult only, though. It's small-ish, with all the water sports and excursions included. Decent price, too.

The bahamas away from Nassau is very safe for kids and away from Resorts. There are many nice homes for rent that are on the beach, or you could try looking on trip advisor for some outisland resorts. Exuma is great for children and is peaceful and quiet. Gopureproperty.com is a good resource for property for sale in Exuma and Long Island