Im wondering if theres any hidden gems out there, maybe units from China, that offer good performance for under $50?
What amps offer budget price but surprisingly good sound quality?
There are some T-amps with headphone outs.
Edit: there are many makes and models of T-amps, not just the Sonic T. eBay has dozens on them for dirt cheap. Can't vouche for any of them, but they do satisfy your requirement of being dirt cheap.
I can't say anything about it other than it's cheap. It does use the Tripath 2024 chip, which is a good one. I have no idea if the Tripath drives the headphones or if a separate opamp does that.
What headphone do you plan to use, by the way ? The best choice may depend on that.
The FiiO E11 is not bad (other than the annoying limitation that it cannot be used while the batteries are charged), but it is slightly above your budget ($65). Depending on your headphones, a good CMOY may suit your needs. If you can build a DIY amplifier, you could give the O2 a try; without the enclosure/front panel and batteries, it may be cheap enough (see here).
Good performance driving what?
FiiO E5 and E6 are tiny, way under budget, and sound pretty good but can't drive a lot of stuff out there.
Some type of CMoy may be okay, but for the single-supply variants, they are often quite current limited. Some dual-supply CMoy running lowish gain with the right op amp can do pretty well.
You can DIY an O2 without the batteries and without the enclosure (but with the AC/AC adapter for desktop plugged-in operation) for about $50, and that should handily beat most cheap stuff, with enough power to run most current headphones short of HE-6.
You will need something with low output impedance and low noise then. A DIY O2 would be excellent if you can build it. Of the FiiOs, the E11 would be best overall (except for some channel imbalance), but if the price of that is a problem, then the ~$30 E6 may be OK, too.