My husband and I will be flying into Frankfurt in early April for business in Schwabish Hall--about a two hour drive south. We will arrive on a Friday morning, and he doesn't start work until Monday. We'd like to see something else in the region--possibly even another country (France or Belgium) before he begins. And, we will have two other weekends to get some side trips in. We've been to Germany before and toured Heidelburg, Rothenburg, Munich. I really would love to cross a border or two on this trip if possible--either by train or car. Advise from anyone more familiar with travel in Europe than I am? Thanks!
If you want to go to another country in the area, go to Strasbourg, France....a lovely, historical and culturally city. As suggested, Koblenz is a good choice; you'll see Deutsches Eck, the point where the Rhine and the Moselle converge, the historical monument is there, and if you go all the way up to Fortress Ehrenbreitstein, where the DJH hostel is, you'll see this tremendous view of the Moselle and Rhine area and Deutsches Eck.
Germany is more than Heidelburg, Rothenburg, and Munich. I would exploit the places near to Schwäbisch Hall before going so much farther. You're just going to spend all of your time traveling and little time actually seeing things. There is a lot to see around Schwäbisch Hall.
Burg Hohenzollern is not a real old castle. It was built in the mid 1800s for the future Kaiser Wilhelm I, but it is impressive, and there have been castles on that hill for a thousand years. There is one bus (#2) per day from the Bahnhof to the castle. It leaves the station at 11:25. To get there by that time requires leaving Schwäbisch Hall at 7:47, with connections at Hessental and Stuttgart. The return bus is at 16:40 from the bus stop at the bottom of the hill. I didn't use the bus. I arrived earlier and walked into town and took a taxi from the market square.
Other places of interest would be Würzburg, with the Fortress Marienberg and the Residenz, picturesque Bamberg, or Nürnberg, with it's WW II significance. Further east, on the German/Austrian border (Salzach river), at Burghausen, is a very old (>1000 years), well preserved castle.
Have you already been to Prague, Salzburg, Berchtesgaden, Herrenchiemsee? What about Oberammergau, Linderhof, Garmisch-Partenkirche (Zugspitze), and Mittenwald. A little west of there is Füssen and two castles (Hohenschwangau and Neuschwanstein).
If you want a taste of the Alps, take the train to Oberstdorf and the Kleinwalsertal, an Alpine valley that is part of Austria (Vorarlberg) but isolated from Austria by the mountains (beautiful scenery and good hiking). South of Oberstdorf, on Bodensee, is the island city of Lindau and Friedrichshafen, with it's Zeppelin museum.
It's not necessary for you to go so very far.
I'm not a city person, but I have been told that Stuttgart is interesting. You'll be close by. Just south of Stuttgart is the old university town of Tübingen.
You won't be very far from the northern Black Forest. Take the train to Pforzheim, then up the Nagold river. Spend time in the spa at Bad Liebenzell or Nagold. Visit Calw, home of Herman Hesse, go farther up to Freudenstadt, called the capital of the northern Black Forest. There is another spa there. BTW, all of these spas, or Thermen, in German, are coed and "textilefrei" - not for the shy. It's a very pretty ride by train down the Murg river from Freudenstadt to Baden-Baden and a "less threatening" Therme.
East of Stuttgart, on the Bavarian border and the Danube is the town of Ulm. You can climb 600' to the top of the church tower there for a great view all the way to the Alps.
Every place I've mentioned is readily accessible by train.