I like to think that they use the Moon and the ruins of Silver Millenniun and the Command Centre as a hangout for when they need to do something away from home. Maybe Ami setting up experiments, a makeout spot (or more) where others including their parents and grandparents won't find, practicing the violin, storing things like women's magazines and photos of celebrities they like, sparring practice, just their own little properties that won't set you back $500,000/month like a 30 m² apartment in Vancouver will. Silver Millennium would be the inheritance of Princess Serenity anyway, its hers to own and use as she wishes.