You want to sleep in Kreuzberg? That could prove challenging depending on which part of the district you choose. I'm not sure of your budget, but the Ibis Budget chain offer great vale for money, averaging about 55 euro per night. Although not in Kreuzberg, they have hotels at both Alexanderplatz and Wittenberg Platz by kurfurstendamm. Not in Kreuzberg but easily reached by U Bahn. I always stay at the latter and the U1 (or U12 as it is atm due to construction works) is about a 20 minute ride to the Heart of Kreuzberg whether Kotte Tor or Schlesisches Tor.
The Kreuzberg Stations at the eastern end of the U1/U12 tend to be where the 'action' is centred. I would be inclined to give the area around Gorlitzer Park/Bahnhoff a miss both for going out and staying - it aint that nice and plenty of dubious narcotics salesmen loitering about trying to peddle their goods.