Here's how you can find and where you can find the Fatman mini nuke launcher in Fallout 4. First, open up your map and locate to the very north spot the Outpost Zimonja. There, you will find an abandoned camp and a boomer in it which will of course trying and killing you all the way. Get rid of it and you will get a Fatman to loot right there. The nuke will possibly spawn around that precise point, otherwise here's where you will be able to gain it.
Go to the USAF Satellite Olivia Station, descend into the facility once you're there and 1) unlock the door in front of you in case you have enough skills; 2) kill all the enemies in there and get the key from there. The mini nuke is in that room, by the way: enjoy your powerful Fatman by now. You can check out our full Fallout 4 Wiki Page for more how to guides, tips and tricks, collectibles location and many other things.