Bank of America
Bank of America has a Museums on Us program for cardholders where you can enter for free the first full weekend of every month. Museums on Us has been going on for over 25 years and it includes over 225 venues across the U.S.. Scroll down their page to see a list of participating museums by state.
Library
Public libraries have Museum Passes that you can check out for free entry to participating local museums. They also include more than just museums. They can include galleries, botanical gardens, zoos, aquariums, and National Parks. The passes are usually good for a week, can not be placed on hold, and are on a first-come first-serve basis. One pass typically includes free admission for 2 adults, and three or four children. Check your local library for more info and to see a list of participating venues in your area.
Possible Designated Free Days
Additionally, many museums and galleries have designated days where entry is free for the public. This could be one evening per week during certain hours.
Museums for All
The Museums for All is a program for free or reduced admission to participating museums for those with an EBT card.
Some Museums Are Always Free
There are at least 200 museums across that U.S. that are always free such as the Smithsonian Museums and the Getty Museum.