CBR is the closest...so close you can even see Illuminations from the property (it's fun to sit in the pool and watch the fireworks)
Old Port Royale is also fun, and they have a great restaurant called Shutters there that is generally overlooked.
I've stayed there 28 days in the past 2 years, and loved it both time. I do think that you should request for Aruba or Jamaica though. I actually preferred Aruba to Jamaica, but I like being close to the bridge...and those two are so small/close that you pretty much can utilize the pool/bus stops/vending/washing machines at either one.
I'd stay away from Trinindad South and Barbados though. As well as parts of Martinique. Both years I made special room request (for placement), and both years they were met. So, when you reserve the hotel, I'd just put in that you'd like to be in one of those villages.