So wait? Automotive or just transportation technology in general? Because that does make a difference.
If transportation in general, I’ll say the National Museum of the USAF at Wright-Patterson AFB. Some really cool items there, including the only Valkyrie XB-70 in the world, one of only a couple B-36’s left and their Air Force One collection, it’s a great visit.
If Automotive specifically, I’ll call out the Automobile Museum in Auburn, IN. And amazing collection of Auburns, Dusenbergs and Cords.
I’m counting planes, trains, and the rest of the world of transportation here. You can make the argument that the Space Shuttle, from my recommended Air and Space Museum, isn’t technically an “automobile.” I would of course rebut with “It’s the fucking Space Shuttle. Is that not cool to you?”