If your budget is truly $200-$300, then just spring for a 970
PNY VCGGTX9704XPB GeForce GTX 970 4GB 256-Bit GDDR5 PCI Express 3.0 x16 SLI Support Video Card - Newegg.com
30 more bucks and its a LOT more card than anything you would buy for $200-$250. Honestly, if you can't quite afford $330, then I'd just keep using your 560Ti for another few weeks/months until you can afford that extra $30.
Heck, I'd even scrap the aftermarket cooler and put that money towards a 970 if you have to. Or at the very least, get an aftermarket cooler that is $40 less, and put that towards your video card budget. $75 for an aftermarket air cooler is a lot of wasted money, IMHO. You could get something that performs the same for half that price(or less)
The massive leap that you would get from anything that costs $200-$250ish to a Nvidia 970 at $330 is well worth it.