I'm particularly interested in Woodrow Wilson, Franklin Roosevelt, Harry Truman, and all the presidents who might have traveled on state voyages before comfortable air travel.
They would generally be offered accommodations in the captain’s or admiral’s quarters, both for reasons of security (those are restricted parts of the ship) and also space to work and meet with their staffs. USS Iowa famously has a bathtub installed in its captain’s quarters, put there for the use of FDR on his way to and from the Tehran Conference in 1943.
That trip is notable in part for the hapless destroyer William D. Porter accidentally launching a live torpedo at the Iowa during a drill. The ship successfully evaded the fish, but there was brief panic over some sort of assassination plot. The captain and ships’s crew were placed under arrest.
You may be interested in the FIRST trip a President took abroad, which did happen to be aboard a warship.
In 1906 Teddy Roosevelt broke tradition and became the first President to leave the US when he traveled to Panama to insect the progress on the new canal then under construction.
He traveled from DC to Norfolk where he boarded the battleship USS Louisiana which had recently commissioned and come out of the yard after her shakedown cruise and transporting Secretary of War Taft to Cuba. In anticipation of his arrival several cabins in Officer County aft were staked out for his living space, that of his wife as well, and for use as an office. Nothing overly hug was needed to refit the ship, though new furnishing were prioritized for the cabins, but for instance the 3in Gun mounted aft was not removed.
Nor was the official delegation putting anyone out of their rooms, as the cabins would otherwise have been empty unless hosting another official dignitary, like Taft previously, or serving as a flagship. You can even see on this cutaway of her sister the Connecticut where the Admirals cabins were located aft one level below the weather deck and in keeping with the slowly discarded doctrine of bunking the officers aft and the men forward. Though with the evolving nature of ship design, and space limitations that brought meant even here it was a bit more jumbled then in previous classes and the Captain and Admiral would also usually have access to a Sea Cabin close to the bridge or in the super structure to let them be close to the action if needed and these rooms too could host guests.
You may be interested in this new article from the time with additional remarks and a few pictures: http://navsource.org/archives/01/pdf/011940s.pdf
