Dear Trent,
J.J. Astor does not have a grave marker but he is interred in the Astor family vault in the Trinity Cemetery located at Broadway and West 155th Street. Do not be confused with the Trinity Church Cemetery downtown on Wall Street. J.J.'s mother is there, as well as Alexander Hamilton and Robert Fulton but the majority of the Astors chose to be buried uptown. J.J. Astor is buried beneath a stone anchor in the family plot but you will not find his name or dates anywhere on the vault.
Madeleine is buried across the street in a small mausoleum with her mother. The crypt does not have a family name so you will have to ask the cemetery officials for directions. The mausoleum needs some work, as a large tree is now intruding into the granite structure.
A caution - Trinity Cemetery is located in Harlem (Manhattan), so I advise that you do not leave any valuables in your car unattended. The cemetery has security but it is easy for someone to simply hop the two feet high gate that surrounds the cemetery and cause trouble. The area has improved but I still wouldn't take any unnecessary chances.
If you have a chance, continue down Broadway to 106th Street and you will see the Straus memorial fountain.
Best,
Mike Findlay