I'm the same height as you are, and I happily go out nightclubbing in 3" or 4" heels, occasionally in inch and a half to two inch wedgies or kitten heels, and only usually switch to flats when my feet are tired from dancing in heels too long. My legs look nicer in heels, and I love wearing them when I go out to dance at my favorite nightclub.
That being said, if I was going to a mall or grocery store, I would probably wear what the other girls wear - sneakers, lower shooties or boots, etc. . Not so much to be less tall, but because wearing heels in a casual environment like that would be conspicuous and out of place. I haven't yet gone out to that sort of public places en-femme, but I've been carefully observing what the GG's wear and how they walk and act, so when I do, I can blend in successfully.
When I was in college, I dated a girl who was just as tall and big-boned as I was. I knew another girl who was happily married and a good four inches taller than me in her stocking feet. While we may be at the high end of the scale compared to GG's, you and I are still well within the range that normal genetic girls reach in terms of height.
So my thought on the matter is we should do what any tall GG does. Wear what we like, and what is appropriate to the place and time of day, and just own the fact that we are taller than average. If someone remarks on our height, just smile, and reply, "Why yes, I do realize how tall I am. Everyone in my family is rather tall." And then go on about your way, and don't let it bother you.