It isn’t exactly a museum, but the eighth floor tour of the Dept of State in DC is interesting.
If you visit Hampshire College there is the Eric Carle Museum - http://www.carlemuseum.org/
Another in Philly is The Rosenbach - https://rosenbach.org/
Not a museum but wonderful - https://www.fallingwater.org/
For Frank Lloyd Wright fans, the Currier in NH that I mentioned earlier has a FLW house.
http://currier.org/collections/zimmerman-house/
Residences remind me of another museum-like offering in NH:
Canterbury Shaker Village http://www.shakers.org/
And another suggestion - Storm King in New York:
http://stormking.org/
@Dolemite Less well known than Fallingwater is Kentuck Knob, near Fallingwater and also by Frank Lloyd Wright (mentioned in your link). Very interesting.
The Folger Shakespeare Library in DC
http://www.folger.edu/
and the Glass Flowers at Harvard.
https://hmnh.harvard.edu/glass-flowers
Given that it’s only two blocks from Grand Central, I’m not sure this qualifies as “hidden,” but the Morgan Library and Museum http://www.themorgan.org/
The Adirondack Museum that is now called the Adirondack Experience, the museum on Blue Lake. Beautiful hand made canoes. That may not sound interesting but the museum was really nice. https://www.theadkx.org/
And now don’t laugh, but we loved the Spam Museum- http://www.spam.com/museum
Kitschy done well!
@doschicos I love Storm King! Great place to take a picnic, also.
I certainly don’t think that the Frick is hidden, but it DEFINITELY is a gem! Describes itperfectly.
@sherpa I remember visiting the Capuchin crypt in Rome over 40 years ago. Striking, to say the least!
We found the West Point museum to be very interesting:
https://www.westpoint.army.mil/museumWestpoint.html
Actually, the whole garrison is a type of museum and is open to the public for tours. The uniform factory is a favorite stop on the tour. USMA is the only academy that makes all of its uniforms onsite; it’s a fascinating and historic operation, well worth a visit.
Grounds for Sculpture in NJ - wonderful collection of Seward Johnson sculptures in a beautiful garden
Corning Museum of Glass - Corning, New York www.cmog.org
The Dali Musum - St. Pete, FL http://thedali.org/
Bata Shoe Museum - Toronto www.batashoemuseum.ca/
The City Museum (more of a fun house than museum) - St. Louis https://www.citymuseum.org/
Since a house museum was mentioned, I’ll add that any property owned by Historic New England is worth touring, especially if you are a history, archaeology, or decorative arts buff. Also third the recommendation to visit the Peabody Essex Museum in Salem, MA. It’s one of our favorites.
But my all time favorite is the Musee de Cluny in Paris. Medieval history on the site of an ancient Roman bath. What’s not to love?
Fort Monroe Casemate Museum- Hampton, Virginia. Very interesting.
Fort Macon in Atlantic Beach NC has a museum room and beautiful grounds, surrounded by water.
I fourth the Peabody Essex 
and add:
https://florencegriswoldmuseum.org/
The Reynolda House has this upcoming exhibit:
In Las Vegas:
The Mob Museum - History of organized crime in Las Vegas and the US.
Springs Preserve - History, science and nature exhibits. Indoor and outdoor areas with lots of interactive displays.
https://www.springspreserve.org/?noredirect=true
National Atomic Testing Museum - Tells the history of atomic testing at the Nevada Test Site
At Storm King, rent the bikes!
https://nawcc.org/index.php/museum
National Watch & Clock Museum - Columbia, PA in Lancaster County.
A couple of SF Bay area entries:
Asian Art Museum - San Francisco…it’s well known locally but visitors to the city might miss it so I’m calling it out
http://www.asianart.org
Pacific Pinball Museum in Alameda - much fun
https://www.pacificpinball.org
The National Churchill Museum in Fulton, MO is very well done:
https://www.nationalchurchillmuseum.org/
Another Midwest gem is the National World War I Museum and Memorial in Kansas City: