Hi Lauren, Wow, your holiday plans sound great, but have you thought about the distances involved? And the US speed limits? (55mph/65mph depending which state you are in), and they do enforce them. We got caught by the Paige County Sheriff.
We've done 2 long distance driving holidays in the US, the longest, Seatle to San Diago, down I1 took us 3 weeks, stopping off here & there along the way. To do what you've got planed in 15 days is very ambitious, and you probably wont get much sight seeing done. But I'm probably talking complete rubbish, so feel free to ignore me.
On the food front, in big citys its not so bad, you can usually get healthy options. Its when you hit the boonies you might struggle, they only seem to do huge portions, but its normal to ask for a doggie bag. You dont have to eat it
Good luck with everything
Denise