Hi! I lived in Germany for a number of years with my German husband, and spend time there every year. I haven't been to France in a few years, so I'll leave that to others, but I'll comment on Germany.
First, if you are two or more people, I think renting a car is cheaper than trains if you are going any kind of distance. I also haven't taken trains in years because we always get a car. I've driven all over Europe, and it's fine. The only place I don't like driving is eastern Europe, because local police zero in on foreign plates and stop those cars for made-up fines for some supposed transgression. But Germans wont do that! They are too law-abiding. Watch for Einbahnstrasse, one-way streets. And right of way has meaning there.
Many places in Germany don't take credit cards, but I think that's slowly changing. Many restaurants only take cash. One way around the foreign transaction fees is a Capital One credit card, and a Capital One money market account ( I think it's called). You put cash into that account, withdraw it in Europe and there is no fee to do so. When you come home, move any cash back into your regular account.
At restaurants, it's customary to round the bill up slightly, but service is already included. Don't overtip. Really. Also, they will charge you for water, so you may as well get mineral water. If you ask for tap water they will look at you like you are insane. Tap water is perfectly fine to drink, but no one does. Don't know why. If there is something you really want to eat, try to know the German name. One friend of mine went all over Bavaria asking for "Black Forest Cake". She came home and told me no one had any! No one knew what she was talking about because the German name is Schwarzwalder Kirsche Torte. Try some different sausages. Hotdogs were copied from German sausages, but the real thing is so much better, they don't even compare. Bakeries are my favorite! German bread is the best, something I sorely miss here.
Some places I like:
Rothenburg was mentioned. It's old and walled. It's just west of Nürnberg, a beautiful city. Try the Nürnberger Lebkuchen (ginger cookies). North of Rothenburg and southeast of Frankfurt is the city of Würzburg, which has a beautiful palace, the Würzburg Residenz. It was nearly destroyed in early 1945 during the war, but recently rebuilt. It has a wall of mirros like Versailles. It's just beautiful. I know they have tours in English. Be sure to visit the chapel next door.
http://www.residenz-wuerzburg.de/englisch/residenz/index.htm
If you go to Berlin, go see Schloss Sans Souci in Potsdam. It was the home of Frederick the Great, who is buried on the property with his dogs. Apparently he loved his dogs more than his family.
http://www.germanplaces.com/germany/sanssouci-potsdam-sights.html
Several people mentioned Dachau. Also in Berlin is Plötzensee Prison, the prison where political prisoners were executed during the war. If you saw the film Valkyrie, there is a scene where political prisoners were strung up on meathooks. That's Plötzensee. You can still see blood stains in the concrete.
South of Berlin you can visit the town of Wittenberg, where Martin Luther posted his 95 Theses. He's buried there also. It's worth a visit if you happen to be driving by.
Dresden is beautiful also. The rebuilt Frauenkirche is worth seeing, also the Semper Oper (opera house).
The small town of Weimar was the home of Goethe and Schiller. It was not destroyed during the war, so the architecture is intact.
So much to see. If you have more specific regions in mind, or questions, let me know.