There are several Power Armors that you can find in the game. Since you can't transport them, you have to power them up first by installing a Fusion Core, then equip them. While you have them, you can just fast-travel to your main hideout where you can safely leave it. The type of Power Armor you'll find will depend on your level. Since you can get a complete set in the second story mission, don't exert extra effort finding the others so you'll chance upon better quality Power Armors. This applies to the Power Armor parts you can buy, especially from Rowdy of Atom Cats Garage.
If you utilized the infinite caps glitch, it's possible for you to acquire infinite power armor frames from Rowdy or Arturo in Diamond City to build your own power armored community or collection. These vendors restock their inventory after a while, giving you access to buy the same "staple" products in their list, on top of some randomized selections.
This page will track the location of Power Armors you'll find the game. Some of them are abandoned where you can simply install a fusion core then bring them home while some are possibly equipped by raiders or hostile NPCs. To get these power armors, you need to shoot their fusion cores to eject it from the power armor and force the user out.
Rooftop of Museum of Freedom, Concord
This is not missable since you'll get this as part of the story quest "When Freedom Calls". The fusion core is found in the generator in the museum's basement.
Unmarked location, further NE of Red Rocket Truck Stop
After getting the Fusion Core from the Mole Rat Den beside the Red Rocket Truck Stop, head to the NE this time. You may encounter more Mole Rats and Raiders along the way. Just keep following the path to the northeast and traverse through the rocky hills until you reach the road. Cross it and you should find the abandoned Power armor in the unmarked location shown in the map below. The Power Armor runs on Fusion Cores which basically makes it the battery of this very useful and powerful armor. To exit the power armor, press and hold the X button.
This is found in the open container van at the back of one of the cargo trucks in the entrance. It also comes with its own Fusion Core.
Revere Satellite Relay
In the radar tower with makeshift ladders leading to the top of the dish, you'll find a Power Armor frame, Fat-Man, and a steamer trunk containing ammo and weapons
Lake south of the Rotten Landfill
To the south of the Rotten Landfill is a small lake. Head there and you'll see the tail of a fallen fighter plane protruding from the water. To its right is an submerged incomplete Power Armor.
Crashed Train Car, East of Tenpines Bluff
There is an incomplete Power Armor to the east of Tenpines Bluff, at the bottom of the cliff along the railroad. It is locked in a cage. The only way to get to it is by hacking the Advanced terminal in the adjacent blue train car. Upon entering the car, you'll also get a miscellaneous quest to investigate Vault 81 and it will be marked in your map as well.
National Guard Training Yard Armory
The armory's door has a Master-level locked and unlocking it will require several steps. Please refer to the National Guard Training Yard's location page for more details. Take note that retrieving this power armor will also activate a heavily armored sentry bot outside the armory which will engage you immediately on sight so don't attempt this if you're low leveled, under-supplied, or doesn't have powerful weapons in your disposal.
The steps are as follows:
Locked trailer car, Fiddler's Green Trailer Estates
This is found in Fiddler's Green Trailer Estates. There's a master-locked trailer car to the middle-east and has planted mines near the area. There’s a cooking station near it. To open it, you have to get the Fiddler’s Green Trailer Key from a Novice Wall safe in the main building at the center of the trailer park.
Inside the locked trailer is an incomplete Power Armor with Fusion Core, duffel bag, and ammo bag.
Guard House, entrance of Fort Strong
Location: Fort Strong
Military checkpoint, South of Natick Banks
Follow the main road south of Natick Banks and you'll stumble upon a military checkpoint. An incomplete Power Armor (model scaled to your level) can be found here.
Roadside Pines
This raider power armor is located in the small raider outpost of Roadside Pines. You can kill all raiders before they get to use the power armor. After while, if you return to this location, you may find the area occupied again by raiders. One of them may possibly wear another raider armor for you to steal.
Gunners Base, Mass Pike Interchange
In Mass Pike Interchange, you'll find the Gunner Commander in the far end of the base and its possible that he won't join the firefight, allowing you to critically injure him or kill him with a sneak snipe or attack. There's a power armor here that can be equipped by the Gunner Commander. Make sure to kill him before he gets in the armor. If he gets in, it will be difficult for you to forcibly eject him unless you can target his power armor's fusion core. If you killed him with the power armor on, you can still get the parts however you won't be able to acquire the frame.
Federal Surveillance Center K-21B
This power armor is located in the bottom floor of the secret government facility. Refer to the location's page for more information about the installation.
Swamp area, SW of Suffolk County Charter
Head SW of the Suffolk County school and you'll find a crashed vertibird in the swamp. You'll find this Power armor beside it.
Destroyed military convoy, west of Finch Farm
In the main road west of Finch Farm, you'll find a trailer truck with two tank escorts. Inside the truck is an incomplete Power armor set.
Dead End Room in the quest "The Big Dig"
In the later part of the quest "The Big Dig", you'll reach a chamber with two fragile walls that Sonya can blast off. The room to the NE leads to a dead-end with a lone Mirelurk King. Kill it to get the free Power Armor.
Crashed Bomber
In the hill between West Everett Estates and Poseiden Energy Turbine 18-F, there’s a crashed bomber and a couple of tanks. You’ll find an incomplete Power armor set here.