A small, football-sized nuclear bomb, as rare as it is powerful.
Mini nukes are now much easier to come by than in past Fallout titles. They are carried by the fairly common super mutant suicider and appear far more often as fixed loot in certain locations (which tend to respawn often when not playing in Survival mode).
Croup Manor - In the basement sitting on a couch next to the staircase.
Diamond City - One can be found in Arturo's house opposite the bed on the table. One must pick the lock to his house and steal it.
Dunwich Borers - Two are located at the bottom of the watery pit at the end of the dig site after the named feral ghouls, they are sitting on an altar next to the unique melee weapon Kremvh's Tooth. Another is located in a small crevice in the rocks, near a raider base at the bottom of the steps down from Station 3, just before the area with the ghouls.
Super mutant suiciders intrinsically carry mini nukes with them. If it is killed without hitting its right arm and before it can detonate the held mini nuke, it can be looted off its corpse afterward.
In the town of Lexington, there is a regularly respawning raider in power armor equipped with a Fat Man on the bridge between two buildings overlooking the town square. Upon death, a mini nuke can be found in his inventory.
Mini nukes can be bought from dedicated weapons merchants (including weapon emporiums built in settlements).
Mini nukes can (rarely) be found in ammo boxes. When found, they will contain either 3 or 4 mini nukes, depending on the player character's Scrounger perk rank.
There is also a mini nuke melee weapon. It can only be acquired by using the console (PC) to either add it to the inventory (player.additem 10e689 1) or by visiting the room that contains every item in the game (coc qasmoke). It cannot be modded in any way. The weapon uses base punching animations and is lazily mounted on the player character's right hand. It has no weight and thus will not risk encumbering the Sole Survivor.