I'll be traveling in Germany in June. Toward the end of the trip, we'll be going to Regensburg and then we have three days before we have to be in Frankfurt to fly home. I'm looking for suggestions for places to visit, places that we can get to via public transport, during those three days. Architecture (esp. churches) and libraries/museums are some of the things we like to see when we travel. We're also open to interesting food experiences. :)
If you like museums, you might consider to spend some time in Frankfurt. One of its main attractions is the Museumsufer ...
Nürnberg is on the way from Regensburg to Frankfurt. by train it is one hour from the former and two hours from the latter. It is a very interesting city. It has an old town, a castle, ..., but also megalomanic Nazi architecture.
Well, Nuremberg (Nürnberg) and Würzburg are the two spots on the way to Frankfurt/M. Bamberg is also beautiful, but I am not sure if it is really worth a detour.
My favourite place in the countryside of Regensburg is Kallmünz (bus no. 15). A beautiful medieval village with a castle and a view over two rivers. And when you're there you have to enter the Bürstenbinder pub. Another medieval house, they sell their local beer of this region ("Zoigl"). Their only meal is "Baustecheala", noodles made of potatoes with huge amounts of oil.
If the Walhalla Memorial is on your list anyway, you could extend your trip: Go there by bike or bus (no. 5, check the schedule in advance, esp. the way back!). This gives you more time to stay there than going by ship would. Bring some food, take a break and watch the ships go by on the Danube. By the way, no need to enter the building except you are extraordinary interested in and familiar to German history. After the Walhalla Memorial take the path away from tourists to the east down the hill and along the Danube to the village Bach (8km), whose wine will definitely be an experience. Don't forget to bring some Aspirin and don't tell me I did not warn you.
Or you could take a walk on the Winzerer Höhen (beautiful view over Regensburg) to Adlersberg and have the famous local beer of this village. Or just ask for the many other small local breweries in the county of Regensburg.
You got already some good answers, I can advice you too to visit Nuremberg.
Another city worth seeing is Heidelberg.It's 1,5 hours from Frankfurt by train and you can visit it at the end of your trip. The castle is the most popular attraction, the old town is also very beautiful. My favorite place is the Philosophenweg on the other side of the Neckar river with its wonderful view of Heidelberg
Regensburg is in easy day trip range of Nuremberg (Nürnberg), Augsburg and Munich (München), and on the way to Frankfurt, you'll pass Würzburg. Each of these cities has all the things you mention and is well worth visiting.
Another place worth seeing is the historical town of Rothenburg ob der Tauber.
Another option is Bayreuth, especially if you are into Wagner :-)