Old tape decks in working condition are good fun, and whether or not they qualify as "audiophile" they can sound GREAT. Very warm, liquid sound quality. The antithesis of dry, analytical hifi sound. It’s a lot of fun. You may notice the rolloff in treble, depending on what tape & deck you’re running. For my older decks, I found that adding Tannoy superwteeters helped with this, even as they were "too much" for my vinyl and CDs.
I had a Pioneer 1020L that sounded GREAT until a channel went out. They should still be findable, in good order, under 1000.
I now have a Pioneer RT909 that also sounds great, but probably not better than the cheaper 1020. These cost more than 1000, but should be findable at or under 2000. The RT707 mentioned above should be a great option; its limitation being the smaller reel size. There are other, less desirable 1970's R2R decks I've heard hooked up, and they sounded great too! One blew a cap WHILE we were enjoying it so...that's a risk.
The decks I’ve had were quarter track (2-sided stereo), quarter-inch tape with top speed 7.5 IPS. I don’t have any 15 IPS tapes. The 7.5 IPS sounds really good - even being needledrop tapes from another audiophile. Below 7.5 IPS is where it loses the magic for me. High end / audiophile stuff is typically 15 IPS.
The stock output levels of these tapes decks is quite low. So it helps to have a good preamp with some extra gain to spare.
The audiophile / studio decks and tapes move up to half-track (one-side stereo), 15 IPS, etc. That’s a lot more tape, and audiophile tape issues are obnoxiously expensive ($400+ a tape), and extremely limited in content. They sound amazing, though! The new tape decks are very expensive, understandably so.