I liked the Hampton when I stayed there,

Apollo Splash Club is supposed to be a very good sauna (never been myself, only walked past). It is walkable from the Hampton (at least if you otherwise are fit for what probably goes on there...) Turn right from the hotel on Uhlandstrasse, then right on Kantstrasse and walk along Kantstrasse, which at the Gedächtniskirche leads into Budapester Strasse and then into Kurfürstenstrasse. AFAIR it's on your right, near the corner where Budapester, Nürnberger and Kurfürsten Strassen meet.

Lot of gay nightlife around Nollendorfplatz, e.g. in Motzstrasse, This is the prewar Christopher-Isherwood-Berlin, and was also the main gay area of old West-Berlin. Lots of good clubs in the east as well, but staying at the Hampton I would start at Apollo and Nollendorf.