The old Art deco style bath: http://www.berlinerbaederbetriebe.de/index.php?id=77
It is next to the underground station U-Rathaus Neuköln. It is beautiful and I can only recommend to use the sauna at least once.

Probably your next schwimmbad with a 50-m swimming pool is: http://www.berlinerbaederbetriebe.de/index.php?id=76

I've never been there but my girl friend visit this for fitness-swimming quite often. You should easily reach it from the hilton. An overview of all public swimming pools can also be found there: http://www.berlinerbaederbetriebe.de/index.php?id=12
However they don't have any english information. You should just ask one week before you travel again, so that a German can check whether there is scheduled maintance.
cheers
757DUD