I don't know where you are or how short your neighbors cut their lawn
but for an answer, in July, look at your lawn and then look at your
neighbors lawn.
I agree there. My lazy neighbors let it get way too long, then scalp
it down to nothing. This way they only have to mow about every 10-14
days. Needless to say, the first dry spell and they have a brown
lawn.
I keep mine at 3" and mow when it's about 4". I don't mow just
because someone else is mowing theirs, or because it's Saturday, or
whatever. 3" is nice and thick, and if it gets a little shaggy after
only a few days, it doesn't bother me. I also edge, which gives it a
very manicured look. It also tricks the eye into thinking the lawn
was just mowed (I think), which lets me get away with longer grass.