What kind of budget do you have for your accommodations? Hard to make specific recommendations without knowing how much you are willing to spend.
That said, to get what you want on St. Kitts you'll want to stay in the Frigate Bay area where you'll have easy access to both Atlantic side and Caribbean side beaches, several different hotels and lots of rental condos to choose from plus there are more than a dozen restaurants and beach bars all within walking distance. Check out Timothy Beach Resort, Marriott Resort and The Royal St. Kitts.
On Nevis everything is much more spread out so there's not a lot of places where you can walk to a variety of restaurants. The upscale Four Seasons Resort is the only hotel that is in walking distances of 4 or 5 beach bars. All is not lost, however, because Nevis is a small island so no matter where you stay you'll only be a short cab ride from most places. For access to the best beaches look for places on the western (Caribbean) side of the island. If the Four Seasons is out of your budget range you might want to check Ouale Beach Resort, Nisbet Plantation, Mount Nevis Hotel, Hamilton Condos or Nelson Springs Condos.
