Device to record & playback music ?

If what you want is the closest possible equivalent of a tape deck in terms of user interface and functionality it would probably be a MiniDisc player, like this Sony.

The technology never really caught on outside certain specialized areas, partly because Sony refused to allow the digital files to be downloaded directly. But, it works exactly like a cassette deck except that you're recording to an optical disc, the quality is higher and you have the option of recording from a digital signal as well as analog.

I suggested the MD primarily because I thought it was probably closest in functionality and interface to a tape deck, at least to a cassette deck. It's capable of making a perfect digital copy so the sound of it will be as good as the digital original played back through the same system.

A reel to reel deck would be a great way to preserve the analog character if you're recording from a turntable and that sound is important to you. It would be less convenient but if leaving digital out of the equation is what you want, it's a good way to go.

I haven't used the Tascam, Korg or Alesis units recommended by Ajahu and Dopogue but I'm sure they have their own advantages. CDR and CDR-W blank media are going to be easier to find and cheaper than minidiscs.