How about an Internet-Radio-Receiver - cheap, not $300.
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- Macintsosh LC, LC II or LC III
- Ethernet Card for LC
- System 7.1
- Open Transport, QuickTime 4, Sound Manager
Just put it together, download a .PLS or .M3U file som the Internet for a stream at modemquality sound and setup MpegDec to startup with that file, as described in the documentation.
The computer will not have monitor or keybord/mouse hanging on the wall. Turn it on, and wait for the music to play, and just turn it off when you go to bed.