Do certain shops stock them often? Do certain factions grant you a supply of them? Do any set locations respawn them?

best way I've found to find them is to look for all the secret areas in buildings and in tunnels. Explore. Explore. Explore. I think I used my power armor only once and I ran through a whole Fusion Core within 5mins. So after I finished off the super mutants I fast traveled back to Sanctuary to my home-made house, took it off and I've not worn it since. That was two days ago. I'm more of a sneaker anyways, easier to conserve ammo that way. Just Explore, You will find a lot of them after a few dedicated hours of exploring.

I've picked up six or seven fusion cores so far and all but two came out of power generators that were still operating.

Same problem cant find any fusion cores, what kind of "fusion" is it that runs out in 5 minutes? Think they need to patch the fusion cores to last longer since they run out way to fast and their not anywhere anyone is able to find.

Once you get to the big city and advanced factions they will always stock them

I found a locked ammo can with 4 and then just went through the door next to it and found another in a generator.

I've not bought any because I'm poor but I've seen some of the Vendors selling as many as 5 of them.

I think the robot in the Goodneighbor gun store sells some. Not 100% sure.

Gun shop in Diamond city always has 4 for sale and restocks them regularly.

Trashcan Carla has a few, as well as the lil diner owner Trudy, there is also one in a junkyard and in the toy factory. They're a little bit expensive though so exploring may be the cheaper route to keep up with your demand.

At the southern end of the map is a place called "the Atom Cats garage".

These guys are a power armor group you can kinda join, and they have a merchant that always has like 3-4 power cores for sale.

Locations will reset after some time with different loot. if it had fusion cores, those will be back too. Happy hunting.

Brotherhood of steel Vendor always has about 6-7

Sentry bots drop them

Higher level raiders who wear power armour (And anybody else who wears it) have them

They can be found in generators in a lot of buildings

Random vendors may have them from time to time

I have about 15 and have never gone below 10, they are easy to find if you know where to look.

heh I have like 20 of them and 2 sets of power armor. could of had 5 sets, but couldnt get them off the raiders. kinda stinks you can't take the PA frames after killing people in them

I'm not a fire from the hip guy so though the power armor and minigun are neat, the fusion cores seem like it makes it more trouble than it's worth.

What kind of price are we looking at for a core?

Don't sweat it OP, power cores become a dime a dozen by the middle of the game. Just explore, or buy them from the four to five different merchants that sell em.