The power armor is located on the lowest floor. Inside you will see a bunch of Synths who will ignore you if you are part of The Institute.
You can access it through a trapdoor in the Abandoned Shack towards the West. In installtion K-21B at the Glowing Sea.Levelled spots: What Power Armor you find at these locations depends on your Level: Beware There is a assultron and sentry-bot at the top! You can also find the full suit (depending on your level) at the top level of the 35 court building, which can be located downtown Boston by the custom house tower. Inside press the red button on the wall in each room to open a glass cell with the armor inside. Take the elevator to go up and fight the robots that attack to reveal hidden rooms. On the coast to the East of Diamond City - Near the Custom House Tower, in a building called 'Court 35'.A terminal (expert) needs to be hacked to have access. In a small secured area at the back of South Boston Military Checkpoint.(You can only buy from Rowdy after doing some favors for them.)
Generally you are more likely to find these at Level 28+ Note: Note: Your character level affects your chances of finding parts of this armor. Below is a list of locations where you can find