I just saw the movie National Treasure and half the movie is set in the Smithsonian (because they have to steal the Declaration of Independence - cool! Not the stealing just the history aspect). There is also two small parts that are set at the Liberty Bell House Place (the true name escapes me right now) and the Benjamin Franklin Institute Place (yeah, forgot this name, too). Both are in Philadelphia.
Then, of course, there's Mummy Returns <img src="/images/graemlins/tut.gif" alt="" /> that has a sequence in the British Museum. The first Mummy movie has a lot of scenes in some Museum in Cairo, but I never paid attention to the name.
American President, Mars Attacks and My Fellow Americans were all filmed in the White House, which sort of doubles as a house and a museum. American President has a scene that was shot in the China Room, My Fellow Americans has a scene where the presidents are following (then lead) a tour through the White House and The White House was sieged by aliens <img src="/images/graemlins/beamedup.gif" alt="" /> in Mars Attacks and kids in the tour helped fight them.
Sex and the City had a few episodes where different museums were mentioned, but I think there were more art galleries than museums.
If I can think of any more, I'll post them.