It was Kievan Rus which ruled Crimea before the muslims took it over, not Moscow. Clearly Kiev has the older historical claim to the area.
Rus or Russia had different capitals at different times, the first was Novgorod (near St. Petersburg), then Kiev until Mongols destroyed this city in 1240, later Moscow became the center of Rus/Russia and then St. Petersburg.
This "historical claim" is not owned by a particular city but rather by the Rus (Ukraine with Russia and Belarus as a whole). When Crimea was taken back by Russians about time of American Revolution it had little Christian population, the later migration was primarily from Russia and today majority of people in Crimea want to be part of Russia. And they would be if not Khrushchev gift.