A nice little trip from Darmstadt is of course the scenic Bergstraße route from Darmstadt to Heidelberg between the Rhenian plain and the Odenwald forest, with the grand-ducal summer residence then Battenberg family seat Schloss Heiligenberg at Jugenheim. The area is famous for its orchards and cherry bloom, May is perhaps a little late for that.
I agree with Lochlannach: Go north of Frankfurt to the Taunus Hills and visit the little spa towns (Bad Homburg, Bad Nauheim etc.), they are truly fairytale-like and romantic. The summer nearly two years ago I had the most lovely little Hessian excursion: Arrived in Bad Homburg by train, walked up through the woods to the reconstructed Roman fort at Saalburg, but instead of visiting it I headed into the woods eastwards on the Limeswanderweg (Limes Hiking Way), very well signposted, along the Roman Limes, where you come across ruins of Roman watch towers and forts as well as clearly seeing the Limes itself in the form of a ditch and a mound in the landscape. It was very thought-provoking to look down on the then-Germanic villages on the north side of the Taunus Hills and imagine how the Roman legionaries felt, looking into barbaric Germania and wondering when the barbarians would attack and how they probably traded quite peacefully at the gates and forts in the Limes. Quite interestingly I tumbled across an outpost of a modern army, an enormous Bundeswehr munitions depot (with US Army signs) and then right next to it the Roman fort of Kapersburg, right west of Friedberg. But I headed down to Pfaffenwiesbach and caught a train and bus back to the Rhine Valley from there.
Don't miss the Limes - you can see it many places in the Taunus and the Wetterau, not just at Saalburg. And everywhere it's a lovely excursion into the woods which are so integral to Germany's charm. See https://en.wikipedia.org/wiki/Limes_Germanicus
Just be sure to bring a packed lunch and water when you head into the woods, the Limes runs along the crest of Taunus Hills, as far from any village and shop as possible.
NB the Roman Limes was the border between the Grand Duchy of Hesse and the Duchy of Nassau / Kingdom of Prussia, so you also pass by some old boundary stones right on the limit between the Romans and the barbarians!
Bu wherever you go - Hessen is sooo lovely, das grüne Herz Deutschlands
- the green heart of Germany: https://www.youtube.com/watch?v=QQI_z9dM6Bs