I took a road trip across the USA last Summer. Did 14,450 miles in 6 weeks and lived in the truck. It's the thing I should have done in my 20's (better late than never).
Here's a few photos from the trip:
http://imgur.com/a/tW7FnIf you're set on East Coast in April/May, here are some ideas.
-In Washington D.C., there is the National Cherry Blossom Festival March 20-Apr 12. The current cold weather probably means a later bloom, so it might fit your travel schedule.
http://www.nationalcherryblossomfestival.org/Washington D.C. is beautiful this time of year, and family photos under the trees look great. Just search Google images for "washington cherry blossoms"
-Charlottesville VA area is historic, and is a good home base if you'd like to tour Virginia wine country. This page illustrates opportunities in the local area. The mountains are very pretty also.
http://www.virginiawine.org/regions/central-virginia/-Charleston, SC is beautiful, historic and has some of the best food in the country. As other have said, it's worth the stop. I've had success renting VRBO.com condos downtown, or there are many inns, hotels and B&B's. Lot's to do and see.
-Savannah, GA is also a great stop. Very pretty, historic parks, buildings, and spanish moss hanging from the trees.
If you can wait until late September/early October, I recommend a trip starting in Vermont to see the legendary fall foliage, then over to Newport RI, then down to the Charlottesville VA area to watch the leaves turn orange and taste lots of wine.