That's a lot of travel in a short amount of time.
Fair enough if you really want to go to SF but there are a number of cities on the East Coast/Midwest that would be a lot easier to travel to/from and you would have a great time.
I would skip Atlanta. It's not the nicest city and you'd be better off spending more time in Philly/NYC for touristy things.
Fly into NYC and then fly/drive/train down to Philly for a few days, then back up to NYC for a few days.