Being 6'1" also, this was a serious issue I had to work through. I absolutely love heels, and I tend to wear them every day. I hate flats, having been socially required to wear them for 38 years. They just make me feel too... boy. Not to mention that most of the female style flats make my feel look like boats, which heels do not. But yes, they certainly draw attention. Being passable helps quite a bit, but it's still an issue you have to work past. Wear what you like, I say, and ignore what people think. You'll be more confident in clothing you are comfortable in.