The Lairs of Large Legions of Lads and Lasses

While the Legion of Super-Heroes of the 30th century primarily operated in an upside-down rocket-ship headquarters (larger within that it appears outside due to 4th dimensional science), it later abandoning it to the Legion of Substitute Heroes so they could reside in a more palatial base.

On Earth-Two during the 30th century existed the Bat Belfry, home of that era's Batman aka Brane Taylor. Both the Legion and Brane also utilized time bubbles to visit the present day and other centuries on occasion.