IMHO, the foregoing suggestions were all quite enlighting. My personal favorite as a foreign guest of Germany when I am there is Munich. I also like Koln and enjoyed Berlin as well. Remember, your interests may be different as I travel to Europe regularly and FRA or Munich are usually arrival airports then I use the great DB train system for the rest of my European travel.
My suggestion for you is to grap a travel reference at the library or purchase it your closest Barns&Noble Book store and compare what the "travel experts" recommend with this post and others. Also, they will explain the transportation options you have when in Germany.
Have fun...as I am sure you will.