What's the best audiophile headphones for under $300 (used)?

ABSOLUTELY 1000% NO DOUBT ON THIS PLANET & as already mentioned by @vrao81,the HiFiMan Sundara & you won't have to wear something already worn by someone with unknown hygiene...
HOWEVER,the HiFiMan Ananda Nano can be had right now for $319.00 & is a BIG step up from the Sundara with better staging & deeper bass!

I have about a dozen sets of headphones, with some costing 10 times what your budget is.  Having said that, the cans I listen to the most are the Sennheiser HD6XX.  They are super comfortable and easy to listen to.  The HD6XX is basically a HD650 with a slightly different look.  You can get them for under $200 at Drop.  Get some better earpads and get the Sennheiser balanced cable if your headphone amp supports it and you'll have a great set of cans.

I'm a fan of Beyerdynamic. The DT-770 pro x now has a detachable mini-SLR for easy cable swaps and I have always liked their sound. Sennheiser has some good stuff at that price like the HD6XX. If money if an issue though, you don't need to spend $300 for good sound and comfort. Kiwi Ears Ellipse are $60 and are great open-backs. If you want cheap closed-back, Try the Jade Audio/Fiio JT-1. The look good and sound great but the head strap starts flaking kind of fast. I use them when i mow the lawn because they have great isolation. Good listening doesn't need to break the bank. 

Just picked up a set of phones in this exact price range and I needed closed-back. Did lots of research..boiled things down to the  Beyerdynamic DT-770 Pro X and Sennheiser HD620s.  I chose the latter.  Still breaking them in, sound very good already. 

...and I wanted an open back pair of planars and boiled all the options down to the Hifiman Ananda Nano.  VERY NICE headphones. Great, punchy and extended bass..mids and highs very smooth.  MUCH better than the HD620s  from top to bottom.  But..I did need a pair of closed back phones and for that use..the HD620s are still nice headphones.