There are not any in downtown, but there are some very close by. The Boston Harbor Islands are easily accessible from the aquarium. They have tours and fairy boats that leave from nearby the aquarium and go out to numerous islands that are right in Boston Harbor. You can see them from Boston actually. You can hike and camp overnight on some of the islands. One of the islands has Boston light, which is America's oldest continuously operating lighthouse. You can also visit the lighthouse a couple of times a year as well. But for serious camping, I would probably head further out of city, drive about an hour.
