The i5-6600 (non-overclockable) would not bottleneck the performance of the GTX 1060. So, for an i5-6600K, even at stock speeds, you won't hinder the GTX 1060's graphics capabilities.
If you are certain you do not wish to overclock, then get the non-K version instead.
The i5-6600K, when not OC'd, has a 3.50GHz (base) to 3.90GHz (boost) at 91W TDP. It's currently ~$220.
The i5-6600, has 3.30GHz (base) to 3.90GHz (boost) at only 65W TDP. It's currently ~$210.
Alternatively,
The i5-7600 (7th-gen Kaby Lake), has 3.50GHz (base) to 4.10GHz (boost) at only 65W TDP. It's currently ~$217.
The i5-7500 (7th-gen Kaby Lake), has 3.40GHz (base) to 3.80GHz (boost) at only 65W TDP. It's currently ~$190.
If you decide on a 7th-gen Kaby Lake...