Ok I think I misunderstood there, steered you wrong. Sorry.
But what you could do (if I understand this time) is record your mixes to CD (via your burner) then take that disc, put it into a separate CD player with a tape deck attached, and record from the CD to the tape. That's how we used to do it in the olden days!
Let's see then... something like this would work
Amazon.com: Supersonic Portable MP3/CD Player Double Cassette Recorder and AM/FM Radio with USB Input SC-2020U: MP3 Players & Accessories
The thing is to get an intermediate medium you can use to get the music onto your tapes from the PC. So although you can't do direct PC to tape (though I'm sure there are older decks that will do this with a bit of fiddling) you CAN record onto CD and thence to tape. But you will need something like the above in order to transfer your music from CD to tape, exclusive then of the PC.
It might work with a USB drive too, though you'd need a stereo deck that had a USB input... nah, I'd stick with something simple like the above.