A friend just shared a super cool website with me called MuseumFreeDays.com. It shows which museums are free on what days and it covers six major cities, including Boston, Chicago, Los Angeles, Miami, New York, and San Francisco.
The most thoroughly-covered city is Chicago. There are almost no listings for Boston or Miami. Los Angeles, New York and San Francisco have few calender listings but scroll down and you'll see a long list of museums that are always free.
If you'd like to share info about a free museum or free entry, email firstname.lastname@example.org with the subject "New Free Days Information."
Free museum days by city