(written from a Production point of view)
Tycho Crater is a prominent crater, named for Tycho Brahe, on the Moon. It was mentioned (though misspelled Tycho Carter) in a portion of the Picard family album, created for Star Trek Generations that did not make it on screen. There it appeared on an invitation for the wedding of Beverly Howard and Jack Crusher, the ceremony for which was to take place at the rim of the crater. Its possible that it gave its name to such Lunar locations as Tycho City and Tycho Base.
According to Michael and Denise Okuda, Tycho crater is the youngest large crater on the visible side of the moon. It is also the site where the mysterious monolith was discovered in the science fiction film 2001: A Space Odyssey. ("The Andorian Incident", text commentary, ENT Season 1 DVD special feature)