Suggest the Old Fort - pretty fascinating history of the fort and the importance it had over the entire Caribbean area from 1700s up to mid 1900s.
The Butterfly People art gallery (yes the back area is off limits as is their private garden, but viewable from within the store) with mid-high end wall art collections for sale. (Pictures prohibited)
The Verde Mesa restaurant for awesome lunch/dinner, reasonably priced with fresh ingredients. A small eclectic place near the cruise ship piers but located in a secluded place 1.5 blocks from the Butterfly store. Limited hours.