1 week in Jan/Feb---IMO, choose easy to get to from your area and as far south as possible for warm weather.

After 20+ islands, TCI is our favorite but I wouldn't chance the weather anywhere from the Virgins north until mid March. For years we went at the end of Feb. and were disappointed too many times with the weather. Now we tend to go mid to end of March to TCI.

We loved Anquilla but it takes long to get there and with only 1 week I would choose a quicker flight. $700 to St. Lucia or Grenada? How long does it take, how many changes? Maybe it's just me, but with kids I'd keep that in mind.

That said, Barbados might be a good choice.

this is a bit specific as you haven't chosen your destination, however it's a house i've rented & think could be right for your group.
the house is 3 bedroom 'casa cavu' on tankah bay beach on the maya riviera coast of mexico, just north or tulum.
http://www.locogringo.com/tankah/cavu.html?name=Casa%20Cavu
it's on a quiet beach with only villas (we found coronas & assorted other libations looked very good on this beach), has good snorkeling, a cenote just down the road & a couple small restaurants. the house comes with a couple that live in a tiny house/casita on the property. she does the housekeeping & he does grounds/pool & is a super cook who can be hired for as many dinners as you choose. loads of history/culture & ruins to visit. also tons of to do's for all. you will need a rental car. see locogringo.com
i'd take st. lucia off the list as it's kind of difficult to get around - the kids won't enjoy the long distance drives.
grenada might be good although it doesn't have many beachfront villas.

How about Barbados? We haven’t been there yet but are going there in March. We had some of the same requirements as you, and chose Barbados based upon those requirements. There are plenty of affordable vacation rentals to choose from. We are staying in the South Coast, but if you want something a bit more “quiet” you may be better off in the West Coast.

Here are some websites that have great rentals for you to look at:

http://www.homeaway.com/vacation-rentals/barbados/r18
http://www.vrbo.com/vacation-rentals/caribbean/barbados

You really won't find an island with both.
"corona" commercial beaches are usually on the flat dry scrubby islands, such as Anguilla, Turks and Caicos, Out Islands of Bahamas.

Architecture, history local culture is on the larger islands where the beaches aren't as nice, Dominican Republic, Puerto Rico, Trinidad and Tobago, Mexico.

Mexico is closest to what you're looking for, although the beaches can get crowded. Of course, it's a catch 22, you need crowds for history and architecture, if not, there's nothing there!

Keep in mind also, places like DR and Mexico, dochave the beaches (with crowds though) but to get to history and architecture require traveling, car, excursion, etc.

Hint - you will find air fares will generally be less to the larger islands that can be reached non-stop from the major US International Gateway airports that service the Caribbean - airports like Atlanta, Miami, Charlotte, JFK, etc. thes islands include the Dominican Republic, Jamaica, Puerto Rico, St. Martin, St. Lucia, to name a few. Smaller island that require connecting flights on local commuter airlines (aka " island hoppers") will be much more expensive.

For a good combination of nice beaches and the history and culture you desire look at Barbados, St. Thomas or Puerto Rico.

I'd pass on St. Lucia if you are seeking "Corona Commercial" beaches since you won't find then on that island. The beaches on St. Lucia have dark gray coarse sand except for one small man-made one at one of the island's resorts.

Great tips and suggestions. We'll do more research and narrow our priorities. Thanks so much.

I disagree that all the beaches in St Lucia are all dark grey coarse sand. For example:-

Anse Cochon where TiKaye hotel is located
Reduit Beach where numerous hotels are located eg Rex Royale
Beach of the Rendezvous Hotel
Beach where Windjammer Landing is situated
Vigie Beach etc

Try googling some images.

The dark sand beaches are located in the south of the island whereas the lighter coloured beaches are in the north. The beach made from imported sand is at Jalousie, if I remember correctly, which is in the south and is very beautiful. My issue with St Lucia is I don't see it as a place to mingle with locals and do the self catering thing, groceries are expensive in the Caribbean and I've never seen a supermarket in St Lucia but have never looked for one either since we usually go AI when there.

Barbados is a good option, I know alot of people who rent villas or apartments and self cater. The beaches are calmer on the Caribbean (west side) of the island rather than the south & more how you imagine a Caribbean beach to be. There are some interesting historical buildings on the island too. There are fish & fruit markets all around, it's a great all around first time island.

Grenada might work too, and local people are really friendly and the island is very beautiful, Grand Anse beach is very nice but would not call it uncrowded.