Shh! Don’t call it a basement within earshot of a real estate broker. It’s the “lower level,” puhleeze. No longer an underground space relegated merely to wine cellars, media rooms, or staff quarters, many lower levels are as fabulous as the rest of the house. In fact, because of local height restrictions (32 feet in most cases), lower levels have become as important to the Hamptons house as hedgerows and hydrangeas.