In terms of nice cities these three within driving distance come to mind:
- Würzburg (1.3 hours from Frankfurt)
- Marburg (1 hour from Frankfurt)
- Bamberg (2.5 hours from Frankfurt)
I can support the suggestion with the Saalburg. The Hessenpark (which is about a 25-30 minute drive) from Frankfurt. In terms of castles, Castle Alsbach and Castle Auerbach are both about a 45 minute drive to the South of Frankfurt in the Bergstraße region. The Taunus lies directly to the North-West of Frankfurt. You can take the U3 to the end station Oberursel-Hohemark and start hiking from there.
That being said, two days on a weekend can easily be spent in Frankfurt. You can go swimming in a public swimming facility (Brentanobad is nice), walk through the old town and sit outside in the garden of an apple wine restaurant. You can also take a small river cruise on the Main river. If you're more into swimming lakes, the "Langener Waldsee" is directly to the South of Frankfurt. If you're also into waterskiing and wakeboarding, the Wakeport to the West of the airport is a great place to hang out.