We were there in January, paid $12 for adults and $6 each for the boys (who were 7.5&5 yrs). We sent about an hour in the museum, our youngest found the actual pirate ship display scary as there are "pirate" noises playing in the background and the room is very dark. Outside the pirate ship area are artefacts, information about famous pirates and some neat dioramas. Once you lave the museum, there is a little courtyard with pirate themed areas where you can take pictures. It was an easy walk from the ship, you can find a walking tour of Nassau on Trip Advisor that shows the museum's exact location.
If you like pirates, you may also want to walk up to Fort Fincastle, it was $1 each to get in but it has a beautiful view of the area and some neat history about how they planned to protect the island if it was attacked...which it never was!