Genos does, in fact, have eyes. While they are thought to be mechanical, due to how he "scans" things, the doctor he gets the modifications from makes sure he can remain mostly human despite being a cyborg. This results in his eyes clearly reflecting emotions, such as pain, or how they shrink in size when he's stunned from Saitama's punch

Along with that, he can feel them getting poked, as a safety precaution. I do not think he has to blink them, though.