Keeping in mind that I'm mostly familiar with Germany south of Koln, and I've lived here for more than 6 years now, my choices are probably going to be different. But the issue's more a question of what do you want to see, as that can help to choose an area you'd more likely enjoy. For example, last year i had family over and we specifically visited Munich and Heidelberg because the oldest boy was interested in seeing the universities for possible attendance. Both are very good cities that draw large numbers of tourists, and I enjoy visiting them for multiple reasons, but if I had to choose 3 they wouldn't be my choices.
For cities I like:
Trier, the largest city outside of Rome until 400ad. Roman ruins, great churches, great art, nice parks, WWII is still visible if you know where to look, nice old town, good fests, the river, the castle, etc. Most visitors never scratch the surface.
Nuremburg, huge castle, great oldtown, nice markets all year round and especially come Christmas time, fantastic museums (history, trains, toys, etc), great churches, food, beer, old bookstores, historical sites, all easily accessible. Plus it's one of the best cities I know to walk at night.
For regions I prefer:
Southern Bavaria (centered around Garmisch-Partenkirchen), where you have the Alps, all the neat touristy towns, the castles, the outdoor sports, and the easy access to Austria and Switzerland. I always try to take visitors there. I go on my own.
Lake Konstanz, which has castles, dinosaurs, the lake, the Alps on the south end, the Rhine Falls on the north, Switzerland, Austria, Lichtenstein, really good food, zeppelin rides, museums, Lindau, and the cherry on top; Mainau, This is one of my favorite places to vacation, and I'll spend a week there in the next two months.
The Mosel Valley, longer, and prettier than the "scenic" Rhine, it has more castles, nicer river towns, and better wine. (Sacrilege, I know). This is where I go on weekends, when I'm not in France. From Trier to Koblenz it's fantastic, and this is much more a tourist area for Europeans than Americans.
One last recommendation, for anyone who's ever thought Napa Valley was nice, visit a little place called Bad Durkheim. Multiple Michelin restaurants, top notch accommodations, surrounded by vineyards, quiet, off the main roads, attractive, with over a dozen small towns of the same nature surrounding it, this is one of the places American tourists just don't know. I've lived in Napa, I looking to buy a home here.