Take Mardee's advice and use Nuremberg as a travel base town for Bamberg, Rothenburg, and Regensburg. I should think you'd spend 5 days just on these places. Other interesting day trip destinations s from Nuremberg include Bad Windsheim, Iphofen, Munich and Würzburg. It's quite simple to see how one might spend an entire week or longer in Nuremberg.
What no one has told you yet is that all these day trips will be easier and in the long run cheaper by train.
VGN Tagesticket Plus (day pass) - covers almost all the above destinations, usually by direct train. €22.10 max per day, no parking fees, no gas, no driving or car pick-up/drop-off hassles or traffic jams. Note that travel on Sunday is free if you have bought one of these day passes for Saturday. The map below shows why Nuremberg is such a good base for this region as well as which towns are within the VGN zone and accessible on the Tagesticket Plus.
The Bayern Ticket day pass can cover day trips to Bayreuth, Munich and/or Würzburg.
The normal pricing you see above, while very good, is not as good as the upcoming €49 Ticket, which according to the best sources will actually be a for-real thing starting this spring - and it is good for all of Germany for one month on the same regional trains that the day passes cover, so for train travel, you can completely skip all that day pass information above. Like the day passes, you can buy it at any station.
As for Lindau and Heidelberg... Those are so far afield that you would need to visit those places separately from the others mentioned and separately from each other as well.