Planning can be crazy-making for sure, especially with little time to spend and too many options to see. Even with my fondness for Nuremberg and the other recommendations for making it a home base, flying into there when you have no interest in spending time there doesn't make much sense.
I'm assuming you have checked the routes, times, etc. for your travel (in all the countries you want to visit) on DB Bahn, but in case you haven't, here's the link -- http://reiseauskunft.bahn.de/bin/query.exe/en.
My almost favorite part of using this source is that you can choose the best departure, arrival, travel time option(s) for your trip, click on the red arrow and see all the stops along the way, where you will change trains, how long you will have to do it and more. But my absolute favorite is to click on the "show map" options to graphically see the route.
By the way, taking the bus from the Nuremberg HBF or Regensburg to Prague seems to be the fastest way to get there by about an hour. You can play with the scheduling to Prague from wherever you want to start using the DB Bahn search, too. It includes the bus connections. Except from Munich (where the bus is also the fastest option), you may find that many routes go to Nuremberg to catch the bus for Prague.
Rome2Rio -- http://www.rome2rio.com/ -- is also a great tool to use for how to get to places. A very detailed map will pop up with each transportation option. There are links to get to the places to purchase tickets and to get the precise schedules.
Once you get your Germany schedule worked out, and if you are only going to Prague, Vienna and Budapest, the rest of your logistics may be much easier.