For transportation, I would take the trains and rent a car for a day as needed. In Berlin you're better off staying in the city and taking public transport which is excellent. One day is enough for Frankfurt but as others have mentioned, Heidelberg is a nice day trip. If you know the days and times you will be traveling you can purchase discount train tickets in advance at the Deutche Bahn site web site but once you purchase the discounted ticket, no changes are allowed. It's a good site to see train schedules even if you don't want to purchase tickets in advance. In Berlin, check out the KA DE WE department store (pronounced KAW DAY VAY) and go to the top floor. It's amazing. Gut Fahrt (German for have a good journey).