Girls call the shots on this one. I would date a girl who was 6'0'' but I always hear concerns about wearing heels and being seen with a shorter guy in public. I don't want to fight against the grain like that, she either excepts me or she doesn't.
It wouldn't bother me one bit if the girl is taller than me. In fact if a girl taller than me (which would make her 6'1" or taller) was interested in me, that would be a plus in her favour because it would show that she's okay with dating a man shorter than her. But generally speaking, height isn't an issue at all. It only becomes one when the girl exceeds 7'4" or 7'5". Reason being beyond that height, she probably won't live past 50.