It's a short taxi ride down to Dickenson Bay, for beach time. I would suggest Le Bistro for dinner, closed Mondays.
Cecilia's only opens once or twice a week for dinner, not sure what nights ? Le Bistro is on the way to Dickenson Bay as well but much closer to your B&B. HTH. There is a beach close to the B&B called Jabberwock, about a mile away again you pass it on the way to Dickenson Bay, no facilities though. HTH

http://www.antigualebistro.com/home/

Cecelia's opening times below.

http://highpointantigua.com/