We have been twice, as a family. The first time we stayed at the a and o hotel in friedrichshain, the second we rented an apartment on guenzelstrasse right by the u-bahn. The hotel was very good, and very cheap (it has hostel rooms too, but we stayed in a family hotel room), but we liked having an apartment. However, Friedrichshain was a much better area to be in - more bohemian, more cafes, more nice independent shops. If we went again we would look for an apartment in that area.
And you are correct, the public transport is great, and there's an ipad app which tells you the quickest route, depending on which lines are running/stations are open/work is being done, so it doesn't really matter where you stay as you'll be able to get to where you want to go anyway.
We've stayed at the Adagio apartments (part of the Accor chain) which are just off the Ku'damm so ideal for the western half of the city. But again, location doesn't really matter as the public transport is cheap and fantastic. Oh, would recommend the apartments too! Can usually get cashback through Quidco.