What things do you suggest we do while we visit? Should be try to by train tickets between Berlin, Nuremberg, and Munich before we go? We are going in late October and will be in London 3 nights, fly to Berlin for 3 nights, train to Nuremberg for 2 nights, and train to Munich for 3 nights.
I'd say get the Berlin-Nuremberg tickets 90 days in advance. 58 euro for 2 vs 200 euro walk up price.
Nuremberg-Munich can be done in one hour on an ICE train, 38 euro for 2 vs 110 euro walk up. But you can take slower regional trains taking anywhere from 1 hour 50 minutes to 2 hours and 50 minutes. Using a Nuremberg-Munich regional ticket is 25 euro for 2 (after 9 am weekday or anytime weekends) or a Bayern Ticket for 28 euro, same conditions. These can be bought spur of the moment out of ticket vending machines, or a ticket window for a 2 euro service charge. The Bayern Ticket will allow you to ride the Munich U-bahns, S-bahns, trams and buses for the rest of the day.