It's worth getting off your bike for a moment at the Lauffenmühle in Lauchringen and looking for the small trail down to the Wutach River (just after the bridge, heading towards Oberlauchringen). The waterfall is beautiful and absolutely worth seeing.
Here the Aare flows into the Rhine. Shortly before its mouth it is dammed up to form the Klingnau reservoir, which is also very beautiful and can be cycled around.