Ideas? 3-week summer roadtrip with a one-year old starting from Virginia

[oconee]

Hi all!
It's roadtrip planning time again! I used Roadtrip America back in 2011 when I planned my trip through the West Coast and you guys helped me a lot. It was the trip of my lifetime and saw amazing things!

Now, we are planning to go back to the US in July 2015 with our baby (one-year old by then). The thing is that we need to be in Fairfax, Virginia for a couple of days at the start of our trip and then have 3 weeks to spend travelling.
I don't want to include the Southwest (California, Grand Canyon, Bryce, Monument Valley, etc.) as we have already been there. Also I have been a couple of times to New York so no need to include that either

The thing is that we like to see natural beauty and landscapes over cities and want to travel at a quiet pace this time (drive 2-3 hours/day). As far as accommodation is concerned, we like to combine campsites and motels.

Could you help me with some ideas to start planning my trip? Yellowstone is definitely in our bucket list but I'm not sure how to include it from Fairfax, Virginia. We're also open to take some flights if needed.

Thanks a lot for your help.
Greetings from Barcelona!