Although you can hop between bahamas and T&C, you have to choose your dates wisely, as Bahamas Air only flies to Provo a couple days a week. That's from Nassau, so then you have to figure out which Out Island to do and get there, which may require overnight in Nassau.

First things first, budget! Without that there's too much information to say.

Both have stunning glorious beaches. Provo has terrific restaurants, Bahamas not so much, but has more character. Harbour Island has nice restaurants, the rest are more "rustic". Both have beaches you can have pretty much to yourself.

Also time of year.

If you are looking to beach hop and love having beaches to yourself pick Eleuthera. Check out the link below. We've been to Eleuthera twice and still have many more left to explore. Simply put its littered with stunning beaches. The dining will not be as fine but I think the island has a nice mix of formal and casual restaurants (Turks has better dining). I would not suggest island hopping since there are no convinient inter island flights between the out island. Plus as indicated before, there is no chance you will run out of things to do.


http://www.discover-eleuthera-bahamas.com/bahamas-beaches.html

We'd like to spend roughly $2,500 on a villa/house (vrbo) for a week. We have another $1,000 to spend on meals drinks, etc. Flights $1,000 so we are looking to stay in the $5,000 range. Is there enough to do on Eleuthera for a week (island exploring?) or should we do 5/6 days on Eleuthera and 2 or so days on another Out Island? We don't need fancy restaurants. Just casual good food is fine for us. Is Double Bay on Eleuthera a good place to stay (for beaches and convenience to grocery store/restaurants?)

In my view, there is plenty to explore for a week. The island is long so location is key. Gov Harbor area is central and double bay on the atlantic side is a bit south of Gov Harbor but not a bad choice. Double bay beach is beautiful and there are some nice homes there. Other beaches to explore are club med, cocodimama beach, ten bay, pomponi beach, winding bay. Lighthouse beach in the far south of the island is supposed to be breathtaking (we've never made it there but I've heard folks say its simply breathtaking). Another day you may want to go north and take the ferry over to check out Harbour island (cute town that feels like nantucket with a 3 mile stretch of pink sand beach). You will see the Glass window bridge along the way.