I did a tour from Vermont to New Orleans this past fall, passing through New York. Here's a link to my journal:
http://www.crazyguyonabike.com/doc/5943 A lot of my route was rather tailored to my circumstances so it won't help you much, but some of it might be helpful. If you're willing to go a bit inland, I highly recommend the Natchez Trace Parkway from Nashville to Jackson, MS, then due South to New Orleans. I also recommend the Ridge & Valley region of West Virginia/Virginia: pretty, low traffic, and the valleys all run in the direction you're riding so there's less hill climbing than in the Cumberland Plateau. Also, as someone else mentioned, East Coast Greenway is good for along the East Coast.
Finding legal places to camp can be as simple as stopping at a fire department or church. I personally get a thrill out of finding beautiful or bizarre places to stealth camp. (usually legally)