There are few museums in the true sense. Bob Lund's American Museum of Magic is great, but is located in a small city that is a long long drive from anywhere. The most famous in the United States is The Copperfield Collection in Las Vegas. It is the Metropolitan Museum of Magic--big, and displayed well. The Ken Klosterman collection is also extremely impressive, and Ken enjoys having visitors take a look. Ray Goulet has an official museum in Watertown, Massachusetts near Boston that has beautiful items on display, and a huge amount of stuff crammed into a small space. The official Houdini museum in Appleton Wisconsin has some items of interest to Houdini buffs.
What there really are in the United States (and the rest of the world, for that matter) are a wonderful group of collectors with large private museums that they are often willing to open to interested individuals: Jacques Voignier in Paris, Bob Read in London, Volker Huber in Germany. There are many others.