The isabella Stewart Gardner Museum announced it's re-opening to the public on July 15, although, as you might expect, with more limited capacity, a requirement to reserve tickets and the need to wear face masks.
The New England Aquarium announced it will re-open on July 16, also with reduced capacity, creation of a one-way path for seeing stuff and the suspension of all interactive exhibits. Facial coverings? Of course.
The Museum of Science says it will re-open on July 26; no details yet, except, of course, you'll need to cover your face.
Other museums have yet to say when they will re-open.