Look at accommodations (resorts or rental villas and condos) in the Frigate Bay area. Depending on where in Frigate Bay you choose you'll be within walking distance (or 2 to 3 minute drive) of both Atlantic & Caribbean side beaches and a dozen or so restaurants and beach bars.

Or, if you don't mind driving a bit (say 15 to 30 minutes) to reach restaurants and shops look at villa rentals in Christophe Harbor and Turtle Beach.

Just so you know, the best "swimming beaches" (with facilities) on the island are at Frigate Bay, South Friars Beach and Cockleshell. Other nice swimming beaches (without facilities) are Whitehouse Bay and Major's Bay - all of the above are located on the island's southern peninsula.