I'm new to the forums but thought I'd jump in here....

I like to 2nd the Outer Banks suggestion. I vacationed there two years ago - stayed in the middle of the islands and biked both directions - it was great!

Also, another 2nd for Womantours. My very first bike tour was with them (several) years ago, and I just signed up for their Glacier NP tour next July (I need something to look forward to to get me through the winter).

Weather will be iffy if you stay in the east, but if that doesn't bother you, there are lots of choices!