Don't wander the wasteland picking up scraps here and there. Here's a location guaranteed to give you the complete armour set.
But there's one suit of Power Armor that's significantly better than the rest. The X-01 Power Armor is the daddy, offering the great defensive and offensive capabilities. Unfortunately it's difficult to find the complete armor set in one place. You're likely to pick up parts of the armor - leg, helmet, torso - as you wander the wasteland in different locations.
Your finds are random too, and you have a better chance of picking up parts of the suit once you start hitting level 30 and more. But there is another, easier way...
Where to find X-01 Power Armor
There is one location in the Commonwealth that houses a complete set of X-01 Power Armor. Here's how to find it.
Firstly, arm yourself with some heavy firepower to make light work of some of the more difficult enemies. Now you need to head to an unmarked location on the map called Court 35. It's in the East of the Commonwealth. Here's the location on the Pip-Boy map - look at the biggest arrow, not the one pointing to Faneuil Hall.
If you've already discovered Custom House Tower just fast-travel from there and head West. It has a couple of turrets protecting it, so take them out first.
Enter the building in Sneak mode for good measure. You want to ride the elevator, but first loot the bodies and the safe in the room to the right, being careful to disarm the laser tripmine. Now arm something lethal, and get inside the elevator.
Threre's a little room to the left with a safe you can loot, but the real prize is up on the roof. As you make your way up there you'll be attacked by an Assaultron and a Sentry Robot. Break out the big guns.
Tip: Head down to the lower floor to fight the Assaultron on its own as the Sentry can't get down. Use General Chaos' Revenge if you have it, it's good for slicing robots. Mines are also good at this point - if you're quick you can lay them outside one of the rooms where the robots come from and do early damage.
Once the robots are dead you'll see the armour in a little building on the roof. To the left and right are the chambers where the two guard robots came from. Go into each of those and press the red button, unlocking the X-01 Power Armor in the middle building.
Congratualtions, you now have the best armor in the game! Power it using the Fusion Cells you looted of the Sentry Robot and you're good to go. Why not test how tough it makes you by jumping off the roof. That feels good, right?