1) Before you do anything, get on a trolley. Take the trolley tour around Salem to get the lay of the land. I recommend a trolley tour to everyone and anyone visiting Salem or any destination for the first time. Learn what's out there - see the landscape - hear the history. And then you are prepared for your day of exploration. Salem has two trolleys - CityView Trolleys of Salem and Salem Trolley. Both provide excellent service and tours, and both offer tickets that are good for the whole day so you can use them for on-and-off shuttle service.
2) Hit the Peabody Essex Museum and plan to spend some time. Upon arrival, purchase tickets to tour Yin Yu Tang, a Chinese House, because the kids will love it, and their perspective will probably be completely different from yours. The galleries at the museum are wonderful. My kids love the Maritime Art, especially the huge model of the Friendship. Check out the PEM's calendar online because they often have special programming for families. Programming or not, visit the Art & Nature exhibit, where the whole family can engage in games and activities that relate to current exhibits.