http://fallout.wikia.com/wiki/File:Fallout_4_-_Power_Armor_Frames_Map.png
I don't know if there is a specific location, but it does seem that the higher your level, the more likely you are to find higher level variants of armor in the Commonwealth. I was level 30-something (under 35) when I found a PA frame by Fort Strong with pieces of X01.
Locations of X-01 armor http://www.gosunoob.com/fallout-4/where-to-find-x-01-power-armor/. Trader at Atom Cats "mieeeewww" may have some spareparts in inventory. You need to wait until her inventory refreshes.
Cheers,
-Klevs
xo-1 armor will spawn at 35 court after level 27, but there seems to be a glitch when looking at the armor, it will appear to be t60 until you enter the armor and once you retrieve it, you'll see that it is in fact x0-1. The first time I went there, I was like....oh [censored], I don't want t60 armor, I already have a set. Then when I went to take the core out of it, that's when I noticed it was x0-1 armor.
Im level 53 and 3 out of the last 5 frames I got were x01. On a side note I found power armour at a raider base and managed to enter it before any of the raiders. Shows that I had to steal it but they are all dead now, how the heck do you claim this as yours now.
I did not know about the PA level thing, so I missed about 2 locations. Had to be in service for Minutemen so I have 1 complete set. Even x-01 is the one with highest dmg resist, some other PA may works as well.
A short story when I forgot to remove the fusion core. Sanctuary was attacked by a single insect (close the to the river). Alarm went off and everyone ran to the river bank just to kill the single insect. We manage to kill it, but when I came back to the workshop to do stuffs, I met Sheffield in power armor and he said "Thank you!, It's like I can finally think straight".
Cheers,
-Klevs
I found a full T-51 set there, left by jumping straight down, returned to base, got out of my X-01 armor and returned......at which point it had turned into X-01 armor.
That's where my first character found a full set as well.
Haven't been there with my second character yet but I avoided some of the other areas where power armor spawns until I hit level 30 or so and have 1 full set and a two other sets that are both missing the left arm and leg.
I'm not real sure why I collect it. I hardly ever use it. My first character only used it to go to the Glowing Sea. My second character has Lorenzo's serum so she won't even need power armor for that.