After seeing, and participating in several discussion about just what model of PA you can expect to find at various locations I decided to answer the question once and for all.
I made a totally new character and leveled it up to level 50 via the console before leaving Vault 111 for the first time. I went with level 50 just to be well past the level 28 spot where X-01 power armor is what you will find.
I spent around four hours roaming all over the Commonwealth and here is what I came up with.
Every Power Armor Frame had X-01 modules on it with very few exceptions. The first exception was as expected in the Museum of Freedom. But that did not surprise me at all since Sturges has dialog saying its a T-45 set of PA. The only other exception was Fiddlers Green where I found a set of T-60.
I only checked two locations with NPC enemies at them that also have a set of PA out in the open and not locked in a cage. The Federal Ration Stockpile with Raiders had a set of T-60 on the trailer out front. The other was the Mass Pike Interchange Gunners camp where I found a set of T-60 being worn by the commander of that Gunner base.
Before any one asks, I hit all the Military Road Check points and the normal spots for finding PA. Yes even the barge by the Old North Church, South Boston Military Check point, and the one by Watts Electronics had sets of X-01 PA.
Now, unless the game puts some sets out there randomly, when a new game is started, I think I have answered the question of just what you can expect to find when going out to collect Power Armor. It's all going to be level dependent with the few exceptions I have noted.