Imi -- If it were a little later in the year, I would suggest the C&O Canal trail running from Washington, DC, to Cumberland, MD. However, your planned time period might be a little chilly for that route, depending on the weather. The trail also can be muddy in places if the weather has been rainy. Other than the weather, however, it sounds ideal for the kind of trip you are considering. It might be very doable that time of year if the weather is not too cold and/or rainy.

The trail itself is mostly flat and unpaved, with a good surface for riding unless there's been a lot of rain. Lots of places to camp, get food and water, and many towns with hotels, restaurants, and other services along the way.

http://www.bikecando.com/

How's the Bob Jackson working out for you? We communicated when you were considering ordering the bike. Mine is still going strong, and I'm trying to plan a tour on it during October.