Just run as much as you can, as often as you can! Say yes to anything and go with anyone that's offering. It's all about getting out there man, most people here consider the river season from March to November, hell some find ways to run shiz all year long. But anyways here's some great suggestions-
I'm not as familiar with rivers over on the east coast where you are, but any of the rivers pinkturtle mentioned are great. The Gualey, Ocoee, Chatahoochee, etc.
Out west -
Selway, Middle Fork of Salmon, Main Fork of Salmon, Lochsa, Burnt Ranch Gorge, Grand Canyon, Westwater, Cataract Canyon, Yampa, Gates of Lodore, etc.
Zambezi (Zimbabwe), Futaleufu (Chile), Rio Baker (Chile), White Nile (Uganda?), countless amazing rivers in Central America, and if you're really ballsy and looking to finish you're bucketlist by actually kicking the bucket.................Inga rapids on the Congo River (D.R.C.)