There are signposted bicycle routes leading to Friedrichsdorf from all directions, though when I went through Bad Homburg I had some trouble finding my way because either one sign was missing or I overlooked it. (So I went straight ahead at one corner where I should have turned left.)

Bicycle route to Friedrichsdorf
When I finally found the bicycle route from Bad Homburg to Friedrichsdorf it was pleasant and car-free.

Wooden sculpture by the bicycle route
Along the way I saw this wooden sculpture in a field near the bicycle route.
If for some reason you don’t want to go by bicycle, you could always take the train, since Friedrichsdorf is served by three train lines.

Trains at Friedrichsdorf station
The grey HLB train in the foreground, on track 4, is a short diesel-electric train that shuttles between Friedrichsdorf and Friedberg, a distance of 16.4 km on a non-electrified single-track railway line. The journey takes about twenty minutes, including four stops along the way. These trains usually run twice an hour in each direction. HLB stands for Hessische Landesbahn.
The longer red train on track 5 is the S5 to Frankfurt am Main by way of Bad Homburg and Oberursel. This suburban train also runs twice an hour in each direction, stopping at all stations along the way.

TSB train to Grävenwiesbach
This yellow, red and grey train on track 2 is the Taunusbahn (TSB) that runs twice an hour from Bad Homburg by way of Friedrichsdorf to Grävenwiesbach and sometimes on to Brandoberndorf.

Friedrichsdorf train station
The station building no longer has any particular function, but at least it is not being allowed to deteriorate like so many of the smaller stations in Germany. In one wing of the station building there is now a small shop which sells snacks and beverages.
My photos in this post are from 2013. I revised the text in 2018.
See more posts on the town of Friedrichsdorf, Germany.
Wonderful bicycle route. Looks very smooth and even. I’m not much of a cyclist but this one looks like a good ride.