Two recommendations:

First, I live in NC and can recommend the Outer Banks as another scenic, but flatter, option. Of course the Asheville area is also lovely - but I prefer to see it on foot (or from the picture window of a delicious restaurant!). I go on bike tours to enjoy myself, not grunt and curse my way up mountains! (I realize many people feel the opposite, including my BF - and good for them, I say!). And the coast is lovely in the spring - shops and restaurants are open for the season, but the tourist hordes have not yet arrived. Here is a tour company that does bike tours of the Outer Banks, staying at some lovely B&B's - however they are quite expensive, so if it were me I believe I'd cheat by checking out their routes and then planning my own trip. http://www.carolinatailwinds.com/ (They also have Blue Ridge and Shenandoah trips). I think after we pass the Bar exam this summer, BF and I are going to bike and camp our way down the Outer Banks.

Second, this summer I had a wonderful vacation in Northern California that included a bike tour of Napa, organized by Napa Valley Bike Tours (http://www.napavalleybiketours.com/). We just did a day trip, starting with an optional hour-long "serious" ride, followed by a leisurely day of riding from winery to winery, tasting wine at each one. It may have been the most fun day of the year. The company also rented us actual road bikes with clipless pedals, so we felt like the cool tour-ists. I would have loved to spend another day just riding around Napa or Sonoma (parts of which are quite mountainous), stopping in the adorable little towns and gazing at all the grapevines. Then you could do a day or two of riding in the Bay Area - lots of people rent bikes in Sausalito and ride over the Golden Gate Bridge. I've never done this, but my boyfriend has, and still talks about it years later.

Aw, now I'm jealous!