There's a couple around the country, and Joe Santulli of Digital Press Videogames just did a kickstarter that raised a lot of money to start building one on the West Coast. Who knows when work will be underway and started though...
Printable View
We had something like this here in San Jose a couple of years ago. It was held in the Tech Museum. Too bad it was only for a short time. They recycle certain exhibits. Last I went, it was Body World again. Anyway, the exhibit they had showcased consoles new and old. I was slightly disappointed since I literally expected almost everything to show up, being a museum and all. They had all major consoles and handhelds on display though, including the Nomad. I think I remember seeing a series of Game & Watch stuff too. There were tons of cabs set up with consoles inside them ready for play. I remember seeing one rigged up for a SNES with Super Mario Kart, a Game Cube with Sonic Mega Collection, and an area that had a huge screen with 4-player SSBM setup.
The Museum of Play in Rochester NY is the preeminent video game museum in the United States. Though just like the Smithsonian, and I imagine with the Digital Press effort, these organizations are so US-centric that they really do the history of videogaming a disservice