There are usually moorings available off Pope's Island, but you rent them through the water taxi company in New Bedford, rather than through the city-owned marina on the island.
I have not been there for two or three years (can't remember); the only launch service is also the city's tour boat and water taxi. If they're running harbor tours, they don't pick up boaters. Also, they shut down early in the evening.
When I was in New Bedford, which is a fascinating city with a great historic district and a vibrant working waterfront (but high crime), there was no designated dinghy dock, either at Pope's Island or on the city waterfront. However, I was told that the city is developing two dinghy docks, one for Pope's Island and one adjacent to the historic schooner Ernestina
, which is docked permanently, as the USCG has deemed it unsafe for carrying passengers. I ran into a representative of the Port of New Bedford at a boat show in Boston in February, and he assured me that the two dinghy docking areas would be open this season, but I haven't verified it.
If looking for a mooring, try contacting Whaling City Expeditions (www.whalingcityexpeditions.com/whaling-city-harbor-tours.html
), as they are the company that rents moorings and also operates the somewhat sporadic water taxi/launch/harbor tour boat. Their phone number is (508) 984-4979.
BTW, the Whaling Museum is a must-see attraction! According to somebody I met at the Maine Boat Builders Show last March, there are only two world-class whaling museums on Earth: Trondheim, Norway, and New Bedford.
Hope this helps. Enjoy your visit.