Being from Philadelphia, I'd have to agree that it should be a stop between NYC and DC. The original White House and center of government was in Philadelphia before moving to DC and they city has done an excellent job over the last 15 years in making the historical areas very visitor friendly.

It is true that the East Coast is generally very hot and humid in August and early September, although we had a gorgeous end of summer in 2014 (and maybe that will happen again!).

I haven't driven from Seattle to LA but in California, a Mustang drive along the PCH (Pacific Coast Highway) is quite nice!

Good luck with your trip. If you want a guide for a day in Philly, feel free to PM me.