Do both coasts
Hi,
I've lived in NY, Boston, Florida, (Northern) California, and have visited the other cities mentioned. It sounds like a lot of your interests are on the West Coast. If it's within your budget ($350-ish each), I'd recommend flying to California during your trip. Three weeks of northeastern cities, if you don't like art museums and want to see nature doesn't sound worth it to me. Florida is REALLY HOT in September, and it's not the best time to visit the Everglades, which is the most interesting nature (other than many miles of beach). Late April/early May is a good time to visit Florida, I think.
My suggested itinerary:
Arrive NYC (probably cheaper and more choices of flights available)
4-5 days NYC including travel day. Some ideas:
Museum of Broadcasting
Central Park
Bronx Zoo
Natural History Museum
Statue of Liberty (because you "should")
Empire State Building (arrive so you get up to observation just before sunset so you can see view in daytime and nighttime)
etc.
The various "Law and Order" shows, "CSI: NY" and others are shot on location in NY They don't usually advertise locations, but you can look around
Take Train to D.C. (Amtrak along Northeast Corridor isn't an adventure or exciting, but it's fine)
2 days D.C. (including travel day)
Fly D.C. to Los Angeles
7-8 days California including travel days:
Rent car
A few days Los Angeles area (amusement park, studio tour, etc -- lots of on-location TV shows and movies if you can find one)
Drive Rte. 1 to San Francisco (Hearst Castle along the way if you leave very early), stop in Monterrey on way. I think it's fun and spectacular even in a "boring" car, or you can rent a convertible for more $.
San Francisco area 3-4 days:
Wine tasting tour
Muir Woods
Lombard Street
Etc.
Fly from San Francisco to Boston.
A few days Boston. Return to NYC for flight home.