1060 might do 1080p/60 now, but rest assured that by this timne next year, you're gonna be having problems keeping 60 at Ultra.
1070 would give you a much longer lifespan at 1080p, and 1440p.
But since I wanna game at 4K, it's why I'm waiting on the 1080TI. Even then the Titan X (P) is not hitting 60 stable unless you dial down some settings.
Personally, I'd probably get a 1060 for now and play at 1080p until the next generation after the 1080TI. 1080p looks damn good on 4K screens.
There is always the option to set a custom resolution for 4K and make it an ultrawide 3840x1600. Considerably less performance requirement than 4K, and better than 1440p, with no scaling needed. Yeah, you'll have black bars, but when you have an OLED or full array local dimming, the bars should be a complete non issue, and you get an amazing ultrawide presentation.
So let's say you have a 1070/1080/Titan X/1080TI
Set a custom resolution of 3840x1600 (which is the rough equivalent of ultrawide, but closer to actual cinema ratio), and you'll have a movie-like gaming experience. This helps if you're not getting quite 60fps on a certain game. The reduced pixel count from the horizontal bars may push you to 60fps.
Funny how LG is selling a 3840x1600 monitor now. You can just as easily have bought a 4k monitor and done it yourself. Sure, aesthetically, no black bars looks better, but in a dark room, and focusing on the actual games, it won't make a difference. It will still yield the same result.
If you have a 2560x1440 screen, try setting custom res to 2560x1080, and you'll have a 1080p ultrawide on your 1440p monitor, helpful if you can't get 60fps on 1440p.
Those with 1080p screens can set to 1920x810, essentially being a 810p ultrawide. I feel that's too low a res however.
Note, the verical res doesn't have to be what I put. Those are numbers to maintain 21:9. You can set resolutions like 3840x1440, or 3840 x whatever number is less than the standard pixel count if you want, and it will be even MORE ultrawide, at the expense of even less pixels, and bigger black bars. Like I could put say, 1920x400 on a 1080p screen and it will show. Not ideal at all, but it's possible.