This is a wonderful bike route that you can start from your door!  

The 3 rivers are the Rhine, Erft and Ahr.  Each stretch is about 1 day of biking, and there are plenty of places to stay along the way.  The Rhine is big and majestic, the Erft is like following a little canal and the Ahr starts out in rolling hills with beautiful natural attractions.  There are also plenty of cute towns and castles along the way.  Part of the route is shared with the 'Wasserburg' route, or the Water-Castle route, but you will have to look at your map and make detours along the way.

You will pass places like XantencologneSchloss AugustusburgBad MunstereifelAhrweiler.

There is a website (all in German) dedicated to the route, and bike map books (German only)  available in local shops.  The maps are hardly necessary as the route is so well marked, but it helps to find bike shops and things to stop and see along the way. (Use the link ot see a much better map than the rough one on this site!!)