Does anyone here know where I can purchase vintage analog recording equipment, and for generally how much? I am currently assembling an 80's retro metal project, and we're attempting to make the sound on our first demo as authentic as possible.

Music stores that sell used gear, thrift stores, ebay, craigslist. Check local GoodWill stores whenever you're nearby - people often donate old audio and stereo equipment because they prefer newer stuff. Prices vary greatly, as there's cheap stuff and expensive stuff, some stuff retains value better than other stuff. The more you know, the more likely you are to spot bargains, so learning about equipment as much as you can helps.

Thanks! My local Goodwill, which I used to work for, is generally fairly bereft of stereo and audio equipment, although I've never checked my local Craigslist for this sort of thing. My area generally isn't very good for this sort of thing, hence the original post.

Just be aware that tape recorders (open reel or cassette) are high maintenance, the mechanical parts often develop problems over time.

As far as mixing desks go, a lot, if not most of the new ones are still analog.

Exactly what kind of equipment are you looking for? Portastudios, reel to reel? You can get an 8 track portastudio pretty cheap on eBay. But Zodijackyl has a good point, check goodwill. I had a good monitoring setup that I got at a goodwill (stereo power amp and 2 speakers) that sounded good and had plenty of volume, and it lasted about 8 years. I paid $20 for the whole setup.