Stay three nights in Munich and two nights in Berlin. You will get an impression of both and it is nothing but a 45 minutes short hop. You might fly into MUC, continue to TXL (BER) and fly from there to FRA - no problem, Germany is a very accessible country.

You could even do two nights in MUC and FRA and a night in Cologne. The high speed trains go every half hour between FRA and Cologne and they take only about an hour.

I travel between London, DUS, MUC and BER very frequently and see most cities once a week and it is not a problem at all, much easier than eg travelling between IAD, NYC and ORD or SFO and LAX. Check-in times are short (arrive 20-30 minutes before departure is fine in TXL), airports easy and the train system is fantastic. You will for sure enjoy it.