Okay... If this doesn't qualify as a nerd place to go visit, I'll smoke some deathsticks.
The Science Fiction Museum in Seattle is about 50 yards away from the Space Needle, so it's a no-brainer to find. It has two floors devoted to as many aspects of science fiction as they could pack into it. You can listen to the radio broadcast of The War of The Worlds, check out a nice display of futuristic weapons, or look at campy artwork from the time of pulp sci fi.
The interplay of current issues in society with the science fiction of the time is explored. Costumes from various movies and TV shows are displayed. I particularly liked seeing one of the costumes that Anne Francis wore in Forbidden Planet. If you like science fiction, you should definitely try to visit the SFM someday.
http://www.sfhomeworld.org/