"Shocker about Rothenburg though. It's all over the travel dvd's we've seen and most of the package tours at least stop in there on their way by so it looked like a no brainer."
One of the great pleasures from my time of living in Germany was seeing how this modern industrial powerhouse of a nation comfortably coexists side-by-side with it's scenic historic past. You don't even have to look very hard. All throughout the country, and particularly in the south and center of Germany, you can see beautiful old preserved towns that exist in their present state not specifically to attract tourists, but because the residents liked it that way and felt it was worth maintaining.
Now, Rothenburg is pretty, no doubt about it. But you said you specifically want to experience Germany, not just visit. But with all the attention that Rothenburg gets from tourist promotion, the old walled portion of the town nowadays is little more than a place to feed and sell souvenirs to visitors. Nothing wrong with that, but you'll experience little of what makes modern Germany tick.
Like Terry Kathryn, I prefer Dinkelsbühl for the reasons given. Also, whereas Rothenburg isn't nearly as unique as the tourist literature claims, I've never seen another town in Germany where the buildings look quite like Dinkelsbühl. Another Romantic Road town, Nördlingen, even moreso offers a glimpse of the mix of modern and historic Germany. And this is only one small corner of the country...
So, I'm not saying don't go to Rothenburg. Just put it in perspective. If you just want to visit a pretty town, go for it. But if you want to experience Germany... go to Fritzlar, Büdingen, Bad Homburg, Bad Neuenahr-Ahrweiler, Dillenberg, Braunfels, Wetzlar, Heppenheim, Schwäbisch Hall, Bad Wimpfen, Weinheim, Hirschhorn, Marburg, Michelstadt, Memmlingen, etc.
Yeah, you won't necessarily experience much of the real Germany in Füssen either. But Neuschwanstein really is something unique. There's not to many other fantasy castles located in such stunning surroundings.