one EE to an aspiring EE, you should spend at least part of a day in Stuttgart touring the Mercedes-Benz and Porsche museums. both of these companies are renowned for design. I was there last Sunday, and believe me you'd benefit from seeing them, especially the MB museum.

the train ride down from FRA Flughafen or Frankfurt hbf is fairly quick (1 - 2 hours, depending on connections). from Stuttgart hbf you can take the S Bahn metro to Gottlieb-Daimler-Stadion (for MB museum) and Porscheplaatz (Neuwirtz?). I ended up wasting money on a cab to the former because I was running late and didn't have small enough bills for the S-bahn ticket vending machine . note to self: next time make sure have smaller bills and some 1-2 euro coins before leaving airport.