I enjoy playing piano though my style is admittedly very simple.
If I'm singing I'll play the chords with my right hand and the root note with the left hand, alternating between the two to keep the beat.
Or if I'm not singing I'll play the melody with my right hand and the chords with my left, usually something out of a "fake" book that tries to reduce the number of sharps and flats.
I find playing to be very relaxing.