Try something like the Tascam DR-07 or if you have an ipod the Alesis ProTrack.
These are portable field recorders. Excellent stereo sound quality and no need for other technology. just find a good placement for them to capture the essence of the room, your vocals with the piano. You can put the tracks you record right onto a computer and do with as you please, whether that be edit them with a program or just burn them to CD.