Lucy The Elephant is indeed in Margate, another town south of Atlantic City on the same barrier island. There really is no 'nice' section of AC once you leave the boardwalk. The rest of the city is truly economically battered.
There's virtually nothing there that would draw people like us here for anything more than a day visit especially if you live more than an hour or two away.
And would you believe that this is the second busiest Greyhound terminal in the U.S.?