E.P.
Great question! I've had those neighbor kid ringing our doorbell at 8 am on a Sunday morning! What is a parent thinking??? And, when we moved here 10 years ago, we went from "no kids in our immediate area to an amazing number - over twenty in just one cul-de-sac, so I understand the question!
Yes, I know all mom's phone numbers and we do communicate on the phone. Especially when my kids were that age, I would call the parent and say, "My child would love to play with your child today? Can they get together? (This leaves the open-ended question of "your home or my home") I found at that age that my children went to other people's houses more because some kids just don't want to leave their home. If you feel comfortable that your two are walking there, together, have them immediately call you when they arrive. It gets them in that habit. ("Hi Mom, I'm here" "Great. Thank you for calling.") If your child goes there, perhaps the next time, the play date can be at your house. It's not geeky at all...if your child is at someone's home, the parent really is responsible for keeping an eye on them. I know I keep an eye out for the children at my home but - don't assume other parents are doing the same.
If your child is playing on the block. - make sure they tell you exactly where they will be - (i.e. I will be in the cul-de-sac or in "this person's backyard" - two locations at a time, are okay.) . My rule is, if I EVER have to look for my children for more than three minutes - meaning, they are not where they said they would be, they are grounded ONE HOUR for each minute I am searching. Also, no going in anyone's home without permission and many friends may have babysitters in a home, after school. My child cannot go into that home until parents are home - period.
On weekends, kids can call their neighbor/friends on the phone after 9 am on Saturdays or 10:30 am on Sunday (unless - they see their garage is open - then they can ring the bell.) As yours get a little older, if the friends are on the same block, it's okay to ring a doorbell (and get that phone call that they are going to hang out for an hour). You just have to know the parents of your children's friends.
Good luck.
EDIT: Your other post brought up a good scenario about "younger kids being dropped off with older kids". Yes, don't assume that because your oldest is going over to someone's home that it is acceptable for your younger one to go too. Your seven year old may not need nearly as much supervision as your five year old. I know it is hard to leave someone out but it does happen. Sometimes it becomes "babysitting" instead of a play date. If the other parent is agreeable to it - no problem. Your youngest daughter can always be included when the play date is at your home.
Also, I'm so glad that you are on your way to being the "geeky" parent! My children are older than your children (a young teen and a tween) and, yet, I am STILL calling parents when I drop my children off to "hang out" or they go to a party, to make sure that a parent is home, that all parents know the plans, etc... my kids roll their eyes at me but they expect nothing less! There's power in knowing your kid's friends and their parents!