Rent a car in Leipzig and drive to the Harz Mountains. You can ascend the Brocken, the highest peak, via an old-fashioned steam train or hike the trail, your choice. Of course it's long past Walpurgisnacht (when you don't want to be there anyway since it's a drunken party, with tons of trash left behind when I went up on May 3), but consider reading that part of Goethe's
Faust to get into the mood. Plus, there's lots of info in
this wikipedia artlcle with links to trail info.
Eisenach, where I stayed overnight after visiting the Brocken, is the home of the Wartburg Castle, the home of St. Elizabeth in the 13th century and where Luther hid out after the Diet of Worms and translated the Bible into German (the basis for the modern German language). Johann Sebastian Bach was also born in Eisenach. If you don't want tor rent a car, it's still worth a stop on the railroad between Frankfurt and Leipzig, and you'll get plenty of exercise hiking up to the castle.
For me, this trip (RT from Leipzig) was part of visiting the Martin Luther sites (Wittenberg, Eisleben, Eisenach), so if you have interest in the Reformation (500th anniversaryy coming up next year, so this year is a better time to visit) that might be worthwhile)
Do expect plenty of delays on the Autobahn! If you try to schedule too closely, a
stau (traffic jam lasting hours ) is inevitable!
If you're at all into Bach, the Thomaskirche in Leipzig (his grave is in the sanctuary, so he really is decomposing there
) is a must. If you can catch a concert with the Thomanerchor, so much the better.