Kings Wharf/Royal Navy Dockyards is pretty good as cruise ports go. There's a number of attractions walkable from the ship including a Pub, a shopping "mall" with tourist traps, and artisans (clay pots, glassblowing, etc.) There's also a drugstore with snacks and sundries. Transportation from the port works well as the ferries to St. Georges and Hamilton dock there. Also, the bus lines are right off the ship (be sure to get yourself a 2-day or 3-day transportation pass when you get off the ship as those work for both ferries and buses.)
Buses can get you from one end of the island chain (Dockyards) to the other (St. Georges), but only do that if you have time to burn. Use the ferries for long runs.
St. Georges is worth a visit. Since the cruise ships stopped going there, it's a lot less busy and could use your business. Visit St. Georges and walk over to Tobacco Bay for snorkeling.