Which president's home was The Hermitage?

Which president was nicknamed "Little Ben"? Which president was nicknamed "The Sage of Monticello"? Which president's home was Mount Vernon? Which president's home was Montpelier? Which president's home was Sagamore Hill? Which president's home was Springwood in Hyde Park, New York? Which president's home was Lindenwald? Which president's home was Spiegel Grove?