These avocados are just about right. Do I now store them in the fridge, or on the counter?
Store them at room temperature. They aren’t supposed to be refrigerated unless they are mixed with something.
Fridge them, they will slow down the ripening process a bit for a few days.
That’s what I would do. I often eat half an avocado with lunch and save the second half for the next day in the fridge. There’s usually a bit of browning but the firmness holds.
Definitely fridge unless you plan on using them by tomorrow. Even then it does no harm.
My understanding now is “Fridge, but don’t waste many days”. That was more or less what I had assumed, but I’m glad there’s a semi-consensus.
I keep my avocados on the counter until they are just ripe. If I can’t eat it that day, I put it in the fridge so it won’t continue to ripen and get overripe.
That’s a new one on me. You keep avocados at room temperature if you want them to ripen. If you want to slow ripening, it’s fine to put them in the fridge.
Another vote for fridge, but not too long. To store half of one with limited browning, leave the pit in, paint the exposed flesh with water and press a piece of cling film tightly to it. If you can impede air interacting with it, it will stay remarkably green. Citrus juice is better, but then you have half a cut lemon or lime you have to store, too.
Unless you make a drink with a squeeze to go with your half an avocado. 
Yes, the old Chiquita jingle had the same misleading, old-wives’ advice we’ve all internalized:
“Bananas grow at the equator
So don’t put them in the refrigerator
But it probably isn’t true. How Long Do Avocados Last and How To Ripen Avocados? | StillTasty.com - Your Ultimate Shelf Life Guide
Protip: if tomatoes are ripe, they’re fridgeable if needed, too. How to Store Tomatoes (and Whether to Refrigerate Them)
Agree with Aspenglow. A proper application of cling wrap will keep them good for a surprisingly long time.
Umm… Onion bagel with salmon cream cheese, bacon, red onion and avocado. Yum!
That doesn’t even come close to scanning.
“But bananas like the climate
Of the very, very tropical equator.
So you should never put bananas
In the refrigerator.”
And did you even read the whole article about tomatoes? The non refrigerated tomatoes won hands down in the first blind taste tests. In the second test the “non refrigerated” ones had, in fact, been refrigerated, just not as long.