As always with such open ended questions - it depends what you are interested in!! Art and culture? History and monuments? Partying and nightclubs? Food and wine?

Me personally, I'd perhaps suggest Dresden and/or Hamburg - two quite different cities to give you some variety, both within easy reach of Berlin.

As for getting to Berlin from any of those cities, either trains or planes will be possible from almost all of them - depends on time and money! Bigger cities closer to Berlin will, of course be more convenient.