In May we did a 9 day cycling trip along the Elbe, from Dresden to Magdeburg. Easy riding, so while we personally ride a lot, I wouldn't say one has to be super-fit to do such a trip (and you can ride more or less as you wish). There are a number of bike touring companies in Germany who specialize in "self-guided" bike tours; we used Mecklenburger Radtour. They'll give you a bike and a map, book your hotels, and transport your luggage each day. You could also just rent a bike from the train station but then you'd have to carry all your stuff with you; it was nice just having someone else take care of the bags.
The great thing about cycling the Elbe (besides it being flat) is that you truly get to see the countryside and visit smaller cities/towns along the way, which seems to me to line up nicely with Rick's "through the back door" philosophy. Keeping in mind this was all formerly East Germany, even nearly 30 years after the wall came down, it seemed in the smaller towns that folks were a bit surprised to see American tourists. The Elbe bike path is extremely well signed, and people were very friendly. Two different days we came upon a local fair, just serendipity, nothing we would necessarily have known about or planned for. For those interested in WWII sites, Strehla and Torgau both had monuments for the meeting of the US and Soviet armies over the Elbe in 1945. If you like wine, you go through a fine wine region. If you like beer, well everywhere is good.
Overall, great way to see more of the country and not just hit the (admittedly awesome) cities of Dresden and Berlin.