While a number of battleships met their end at the hand of atomics at Bikini Atoll, likely the only dreadnoughts to carry nuclear weapons for tactical use were the Iowa class.
Those fast battleships “may have” toted such devices in two forms.
Between 1956 and 1962, the Navy had a limited stockpile of about 50 MK-23/W23 nuclear shells for the Iowas‘ 16-inch guns, each with a yield of some 15-20 kilotons, with each ship of the class equipped to carry as many as 10 of these mushroom makers. Of note, Hiroshima’s Little Boy was a 15kt bomb.
Then in the 1980s came TLAM-Ns, the so-called nuclear Tomahawk cruise missile with its W80 150 kiloton warhead. First fielded in selected fleet units, only about 300 made were produced and the Obama administration dismantled them in 2010.
Below is a great video done by the curator of the USS New Jersey (BB-62) Museum, where he shows off the (possibly) TLAM-N related areas of the ship, including the panels, Marine guard post, and ABLs.