A stickler might say it depends on where you and your friend are. If you are both in NYC, coming is better. It you are both in LA, going is better. If either of you is elsewhere, it is pretty much a free-for-all: any combination works. In actual everyday usage, both work fine regardless of where you are.
Since you are such an excellent student, please allow me to comment on something else: "Our moms are church in LA buddies". This word order is not natural. "Our moms are church buddies in LA", and "Our moms are LA church buddies" are natural.