Put the Romantic Road in perspective- it's a bunch of attractive (but not as unique as advertised) towns strung together on a series of routes that roughly parallel the main Autobahn link between two of Germany's most popular regions for tourists- the Mittelrhein, and southern Bavaria. The road itself is not any more scenic than a typical rural secondary route for that area of Germany.
But, you're headed from the Mittelrhein to the Allgäu anyway, so depending on how much time you allot, it makes perfect sense that you might want to explore some of the towns along the way. Most tourists head directly for Rothenburg, which is pretty but a little too overrun with souvenir shops and tour buses for me. I prefer Nördlingen and Dinkesbühl, personally.
For hiking in the Allgäu, Oberstdorf would be my choice for a base. I'm not sure if there's a swimmable lake in the immediate area, but you're not far from the Bodensee. On a good day, the clear blue water and backdrop of the Alps couldn't be more scenic.