This tread will live a little longer...
First I'd like to offer an update on the GTX 650 Ti driving 2160@60Hz. Well, it does do so but at the cost of 4:2:0 vs 4:4:4. Since I'm using this PC as a workstation and 4:4:4 is a must, it's 30Hz for now.
So that the fore mentioned can become a moot point I still intend to upgrade, as was the impetus of the OP. After some additional research inspired by the replies above I'm feeling 1050 or better may be my best option. While the current card handles basic workstation duties just fine a limitation was witnessed this past weekend. 4k media plays smoothly but attempting use of video screen capture, even at a reduced HD window size, results in stuttering and dropped frames. This didn't happen with the HD monitors so I'm guessing the card is being overly taxed at 2160 even though I'm not attempting to do full screen capture. 1GB VRAM probably plays a big part there.
Anyhow, I got stiffed on the $60 1050 card I noted in a previous post but see used and B-stock can often be had for around $100. That got me looking and I see 970 cards abound for about the same price, maybe even a little less. It looks like even though this is an older card it could be considered a tier or two better than the 1050. Unfortunately I see it's also at about double the TDP with twin fans which could negatively impact my desire to quiet-PC as much as possible. So I have to ask -- If I am looking for, at minimum, the performance of a 1050 Ti 4GB and in about the $100 range new/used should I stick with that card or might there be additional options?
EDIT -- I should add I have been an NVIDIA user for quite a few builds now but wouldn't shy away from Radeon's, such as a 560 or so. I really also gravitate towards the single fan form factor.