Go to Oberursel, which is just a few kilometers to the north of Frankfurt and can easily be reached with the S-Bahn from the airport. From the city train station it is an easy walk into the old town (there's a brewery you can go to or a few cafes). From the Oberursel train station take the U3 to the Hohemark end station, where you are at the foot of the Taunus hilly area, where you can easily hike.