The Palomar Mountain Observatory in CA is great if you like star-gazing. Ditto for the Griffith Observatory.

The MoPOP (Museum of Pop Culture) in Seattle.
The Rock'n'Roll Hall of Fame in Cleveland.

Anonymous wrote:chicago
art institute
https://www.artic.edu/

philly
https://philamuseum.org/

houston
menil collection
https://www.menil.org/

boston
isabella stewart gardner
https://www.gardnermuseum.org/experience/collection

harvard glass flowers
https://www.hmnh.harvard.edu/glass-flowers

I LOVE the Isabella Stewart Gardner museum.

This is not going to be relevant to OP, but the Indianapolis Children's Museum is by far the best Children's Museum I've seen. I went as a child and still remember it. I don't live anywhere near Indiana, but I'm trying to plan a trip there for my own kids.

I second the Philadelphia Museum of Art and Mutter. If you like ships, Independence Seaport Museum, also in Philly, was a blast for me! Got to walk around an actual submarine, so cool!

It's super out of the way but the Maine Mineral and Gem Museum in Bethel was a really cool find! It's quite small but it was super cool.

Portland Museum of Art (Maine) was also a lot of fun!

As a DC kid, I always enjoyed the U.S. Navy Museum in the Navy Yard more than Smithsonian museums. Is it still off the beaten path?