Actually RB -
There is a great route from Savannah thru Camden, Ala - then veering NW thru northern Miss crossing Old Man River at Helena - home of the Delta Blues. From Helena you can cut up thru the Ozarks in Ark and the Flint Hills in Kansas to Manhattan.
From there you can take many pleasant and quiet backroads west - depending on where you plan on ending up. Late spring / early summer isn't such a bad time temperature-wise in the eastern 1/2 of the U.S., but you are likely to have a good deal of rain - with big, dangerous, thunder boomers out on the plains.
There are a number of ways to get to northern Calif in mid-summer without roasting. If you are planning to head out to Oregon or Wash - there are even more choices.