I like your plans very much. Get out of LA as fast as you can - not our nicest city (my opinion). Be sure to stop off here in Portland on your way to Seattle (just 3 hours south - you must travel right through Portland to get to Seattle) - Portland is a very mellow town - you will enjoy! In Seattle, I would also see the San Juan Islands in Puget Sound, as well as travel to both Victoria and Vancouver in British Columbia, Canada (both are really nicer than Seattle itself). Ferries travel frequently on Puget Sound (see websites for both Washington State Ferries and British Columbia Ferries). Amtrak can also get you from Seattle to Vancouver. Amtrak is a good way for foreign tourists to see our country, but don't expect a great deal of comfort, and the food is terrible and expensive (bring your own to eat well). Be sure to stop off for a day or 2 at Glacier National Park (see the National Park Service website) - the train stops at the park. The rest of the trip across the Great Plains will be a little boring, but you will enjoy the Minneapolis/ St. Paul area. Are you continuing to Chicago? - a huge city, but very good for shopping, and excellent transportation facilities. Book your Amtrak reservations well ahead, since summer is prime travel period, and this means of travel has become very popular recently.
By the way, you will fall in love with San Francisco (I lived there 25 years). Be sure to see the excellent views from both Twin Peaks (above the Castro) and Buena Vista Park (above the Haight). Rent a bike to see Golden Gate Park and the Golden Gate Bridge. SF has the best Asian restaurants in America, but they're not in Chinatown (I like Clement Street in the outer Richmond neighborhood).
[ Edit: Edited on 24-Jan-2009, at 10:46 by Daawgon ]