I live in the burbs, we have both front and back yards set up pretty nicely. Front yard is for when the kid wants to ride bike or mingle with neighbors. Back is for family time and bbq
It is sad how many neighborhoods don’t mingle. We’re lucky, our neighborhood is pretty active and a lot of young kids around my sons age. Not so friendly it’s overbearing but not so to yourself that you feel cut off either.
I used to be a pretty anti-social neighbor, but we moved to a nice 5-house cul-de-sac a couple of years ago and my neighbors are awesome. We're all on first name basis and text each other when we're going out of town, etc. But like you said...not so overbearing that it's awkward either. Really the perfect balance. Anyway, I'm going with back yard by a long shot. Pool, firepit, grill, trampoline in the backyard. Nothing really going on in the front.
My wife prefers the front yard but she will not mow it. I don't mind the back yard. Nothing to mow but sometimes the mud can be a problem if we spend too much time back there.