Twice I have stayed at different Air BnBs in Kreuzberg, not far from Admiralbrücke. Very neighborhoody, untouristy feel.
Once I stayed at Miniloft Apartment Hotel Kreuzberg. They have another hotel in Mitte. The location of Miniloft Kreuzberg was fantastic. Very central. Five minutes walk from U Kochstrasse. I would definitely stay there again.
Another time I stayed way over in City West at the Citadines Kurfürstendamm. I don't recommend staying that far out unless you have a lot of activities planned closer to that side of town, or you get a deal on a place to stay (which is why we stayed there - it was part of a Delta Vacations package). It was fine, transit took us everywhere we wanted to go, but most of what we wanted to do was in the east side of the city.
In March, I stayed at the oft-recommended Adina Apartment Hotel at Hackescher Markt. This location is also fantastic with the added benefit of being able to take the S9 direct from and to the airport. The hotel is modern, and, I thought, a little soulless, but completely comfortable and super convenient to everything.