[OldManTime]

I am looking to borrow, of rent a Reel to Reel tape recorder, to convert old audio reel tapes to files on my puter..

[JoelJohnson]

Call different libraries, you might get lucky and find one.

[villagetinker]

There area few listed on CraigsList. I am assuming that you have suitable inputs on your computer and the suitable software to make the files. Note: this will require lots of time as none of the hardware/software that I have seen is automatic, you need to start the tape player, start the software, then stop the software when the song ends, save, etc. and then repeat. This is why I never got around to taking all my vinyl to digital files.
Good luck with your quest.