I think the previous reply may have been talking about something different. There are transmitters that I have seen and used for this application. They plug into your walkman and have a small antenna to transmit a signal to the FM radio in your car. The one I had and used sucked. Same thing you experienced, poor sound and did not sound like it was in stereo.

An RF modulator actually connects in line with the antenna of your radio. The principle is the same but it cuts out the air interface. The sound quality is going to be better than the aforementioned transmitter, but will only be as good as the FM section in the radio. This is the same sort of arrangement used for some aftermarket cd changers that can attach to factory headunits.

Other options include the tape adapter which I think you said you used and didn't like. An outboard changer is another option. You could use an RF modulated one if they make them that play MP3's or you might try the suggestion of another poster with the direct connect to the head unit. The last, and best option would be a new headunit that plays MP3's. Not cheap, but if quality sound is a priority, you will get what you pay for.