For $220, I'd only look to the used market.
At $220, you're looking at either a 1050TI or a 3GB 1060 and, while both solid options, I don't feel they offer +$220 improvements.
For example:
So, say your 1050 is a $110-$120 GPU.
Generally speaking, at 1080p, a 1050TI is 22% faster, a 3GB 1060 is ~76% faster.
Then, consider you could likely recoup around $80 selling a used 1050.
So, buying a 1050TI = $145, Recouping $80 from selling a 1050.
Net spent = $65
All in all, to end up with a 1050TI you've spent $185 (+54% vs your original card), for 20ish% gains.
Same applies for a 3GB 1060. $215 to buy, recoup $80 = $135 Net. So in the end, you've spend $255 approx (+113% vs original card) for 76ish% gains.
I'd look for a 980TI personally - as you'll actually see a solid value for your total outlay., A 980TI is close in performance to a 1070.
You could also look for Fury's or Fury-X's, but miners have driven their used prices up a bit.
A 980TI is where you start to your true value for money..... with a decent amount of luck.
Recently they've sold for $285. Net spend is going to be $205 ie $325 once you factor in the original cost of the 1050.
$325 is +170% of the 1050 new cost. And performance is pretty much in line at +170% vs a 1050, when you compare across all resolutions - the fact that it's a capable 1440p and (somewhat) 4K too. .