There is a small lake very close which we often go to. The Odenwald region is also not far - that's where we love to go hiking on the weekends. Cycling is very popular in Darmstadt, you can go everywhere by bike. There are tennis courts within walking distance, a gym and mini golf and horse riding.

The places we love in Darmstadt:
Darmstadt is a center of art nouveau which you can see throughout the city. Especially in the area around the Mathildenhöhe. Rosenhöhe also is a park worth visiting, it has a huge rose garden and is always a nice walk.
Then there is the park "Herrngarten", which is a meeting place for everyone in summer. People have their picnics on the lawn, make music and do their outdoor yoga classes there (at Kantplatz around the corner you get the best ice cream ;-).
The artist Friedensreich Hundertwasser designed a house in Darmstadt called the "Waldspirale", it doesn't have any corners - everything is round.
And then there are is the quarter Martinsviertel with lots of nice little shops and cafés.
There is also a great theatre and there are lots of music festivals and city celebrations throughout the year.
The Centralstation which is a concert hall has lots of different events like of course concerts, but also poetry slams, author readings, etc.

In Frankfurt you can also find a large variety of museums.