So, what exactly happened to each location from Fallout 1/2 up until 2281?
I know there are ending sliders that say "X is canon".
But the actual information about this is spread out like crazy.

For example, in Novac you will find out that New Reno is run by the Bishops and that the current boss/don knows the wastes like the back of his hand.
Indicating that the Chosen One banged either the daughter or the wife of the previous boss/don.

What other dialogue do you remember which detail what happened to places in the Core Region?

According to Razz, the Boneyard is a lot like real-life LA, large, bustling, commercially important, but kind of a [censored] place to live. Hanlon retires to Redding. Pretty much all the Caravans are from The Hub. Klamath Bob mentions Klamath is now part of the NCR, meaning they're already in Southern Oregon. The Big Circle is a lot safer, since after you convince Cass to sell the company, if you ask her about going back home, she's kind of "Been there, done that" and the Crimson Caravan employee Henry Jamison came out East looking for adventure and excitement, presumably because this is something he is finding in his boring and safe life back home. That's all I can think of, anyway.

Someone mentions they are from Arroyo. I believe it is the doctor in the clinic outside of New Vegas. If not, it is some doctor. So people from Arroyo have the ability to be doctors.

A bit contradictory, but I think someone said that New Reno is now "Van Graffs and the Wrights" instead of "Mordinos and the Wrights". So I guess it's still run by multiple crime families.