Having had bikes tampered with on previous trips (admittedly not in Germany), I am now paranoid about bikes being left out overnight in open air car parks. I stayed at the Ibis Hotel in Berlin - just 15 mins walk from the Brandenburg Gate. Very swish - with the cleanest & most secure underground car park I've ever used - only accessible via a lift and a personal swipe card. In fact it was probably more secure than my office.

I have their number and address at home, if you need it just PM me. The cost was pretty good too - about £40 per night. Especially if you are interested in history, Berlin is superb - you could easily spend your entire trip there.
Unless you are a map reading God, I would take the GPS. The SP3 took me straight to the hotel, along roads which I doubt I would have found if I was constantly reading a map. The problem is that you would need to stop regularly with detailed maps, just to get the relevant section in the map holder. Generally, the Germans seem more patient and tolerant of driving - even when I did something dull, I wasn't honked once.
The Autobahns are ok if you need to cover big mileage in a short time, but are boring. Keep a very careful eye on your mirrors (especially if changing into their equivalent of lane 3) as some of them are travelling at 120 mph +, which doesn't give a good margin of error. I saw about 6 very very near misses in just 1 week.

Be particularly observant around Antwerp - they are doing major road works there - I ended up in the city, but just could not get back onto the road needed for over an hour. In fairness the GPS was pointing me in the right direction, but all the access roads were blocked off.

Some of the best roads I went on was in the Harz region (mentioned by Dave Hall in this thread:
http://www.ukgser.com/forums/showthread.php?s=&threadid=31256&highlight=german ).
I'm very tempted to go back again - I'm sure you will love it. If you think I can help, just drop me a PM.