My two cents, in no particular order:
- DC in summer is hot and humid, as is much of the country. If you are used to hot and humid summer weather, you'll be fine. The city was built on a malarial swamp, though the swamp and mosquitoes are (mostly) gone. Everything is air conditioned in the US.
- Philly is a worthwhile stop, but having been there many times, I'd do it as a day trip from NYC. It's an hour and 20 minutes by train. If you want to take your time, you can stay overnight. You can see all the political sights in an easy day, however.
- i agree with everything people have said about the beauty of the West Coast. I'll add that, for a slice of Eastern Americana, you should take a day trip from NYC up the Hudson Valley, which is one of the prettiest parts of the country. East Coast US has a markedly different feel than West Coast US. The two excellent historical sights you might check out in that day trip are Hyde Park (home of FDR) and one of the many Vanderbilt estates.
- NYC is in a class by itself as American cities go. You can easily spend a week here and not see it all. I'd budget 3-5 days of your trip in NYC, depending on how many museums you want to see. NYC in summer is also hot and humid, with the delightful odor of rotting garbage wafting through the streets.
- Since you're not really sure what you want to do, I'd strongly suggest getting a good general USA guidebook and using that to plan. You've gotten some good input here (and will continue to do so) but it's good to get a reference lay of the land.
- If you're not going to bother with a convertible anyway, then why not just get a nice car to drive in? I'm not sure I understand the Mustang fascination.
- You could easily spend 3 weeks tooling around the West Coast as well, depending on your priorities.