Heidelberg
Heidelberg is less than an hour by regional commuter train from Frankfurt. A small town, with a population of less than 200k, Heidelberg is considered to be one of German’s most beautiful towns. This historic town is famous for Heidelberg University that was established in the 14th century CE, and the red sandstone ruins of the Heidelberg Castle. Stroll around the old town, especially the town square or the Marktplatz, with its numerous cafes, take a funicular to Konigstuhl for a bird’s eye view of the town and visit the Castle, see the Church of the Holy Spirit and the Heidelberg Tun, a wine barrel built in the 18th century CE and walk over Alte Brucke, the old bridge.
You can even spend a full day if you wish to roam around leisurely.
Alte-Brucke(old bridge) and Castle, Heidelberg, Germany 
Heidelberg castle, Germany
Bad Homburg
Bad Homburg is also less than an hour from Frankfurt by train. You can either take a regional commuter train or take the metro though in that case, there will be a bit of walking to do before you get to the town. Instead of walking, you can take a bus from the metro station. There is nothing great to do, but its nice strolling around marktplatz, the old town(dates back to 8th century CE) and relaxing at one of the spas. Some of the buildings are fabulous though I must say many of the old buildings look pretty much the same everywhere.
