What others have said, plus:

The Speedway Museum, Nebraska. The collection of vintage speed parts and rare engines is unparalleled !
The Auburn Cord Duesenberg Museum in Auburn India will blow you away. Classics galore.
The Brumos Collection in Jacksonville Florida is home to a bunch of vintage Millers, and the Revs institute in Naples Florida if you like vintage race cars.
The Tallahassee Auto Museum is really good.
The Justice Brothers Museum in California is cool.
The NHRA museum at Pomona.
The museum at the Indianapolis Motor Speedway is essential.
The National Packard Museum in Ft. Lauderdale Florida is really good.
The Wheels through time museum in Maggie Valley, NC is really interesting, but is mostly vintage motorcycles. But the way they are displayed is so cool.