IMO a car will give you more flexibility. This means you can choose hotels outside a main city. Germany is full of great small family-run hotels with an excellent restaurant. I travel frequently (for business) throughout Germany and I always try to find such a place. It's easy to check on eg. Hotels.Com.

Even for train travel long-distance rail passes as sold in USA are a rip off. Research cheap fares either on the national rail carrier DB website or an independent provider like Trainline EU. It's worth looking for bargain First Class upgrades. By the way you can usually pick up a rental car at your arrival train station in Germany