You probably won't get many responses because you posted in the Long Island City forum instead of the Long Island forum. Quite a difference.
Hopefully you will have a car at your disposal, if not you can catch a train into the city, About half an hour by train. If you have a car you can travel down to Jones Beach, about 1/2 hour drive, or you can drive out to the hamptons or to the north fork and visit the vinyards, both about 1.5 hours drive
Don't know what you like but I can't think of anything right in Westbury. Places to eat won't be a problem, there are good restaurants everywhere.