You have been given some very good guidance, especially valid is Abalada's take on HD. I have been there many time and lived there for 9 months. You might feel as though you just have too much info bombarding your brain, but don't worry. I have had the best experiences when not trying too hard to "experience" Germany. So here's my .o2$ worth:
Drive up the Nekkar to Dilsberg. Have a beer as you look out over the valley.
Take a tour of Heidelberg castle. Ignore the tourists. Read the cornerstone of the Ritter Hotel and contemplate how old it is. Walk out to the middle of the Old Bridge and stare at the castle. Look up behind the castle and try to figure out which house Mark Twain lived in. Drive to Stuttgart (if your feel like a road trip) and go to the Mercedes museum. It's free and you get to see the world's first car and the world's first motorcycle. It's a nice experience even if you don't care about cars. Another HD day trip, go to Schwetzingen and look at the apsaragas statues and have lunch in the Cafe Journal. Just walk or drive around, have lunch and watch the Germans. Don't try too hard. Just observe and enjoy. Go to a grocery store or their version of Home Depot. Have fun figuring out the language. Enjoy the world's best beer. Just enjoy.