Java: Avoid 'instanceof' when adding or removing items from the list

I'm creating a game. A game has a GameMap. In order to track state of things on the GameMap, I wanted to create ArrayLists for each of those things. The problem is, I don't want to have to create separate methods for adding, or removing items from each type of ArrayList. I'm a newb so of course the first thing I can think of is the 'instanceof' operator.

Keep in mind that, at present, GameMap is a discrete class, and not an interface, or abstract class. The intent is to instantiate a GameMap object when the game is initialized.

public class GameMap {

//GameMap has a name
private String mapName;

//GameMap has rooms
private ArrayList<Room> roomsOnMap;

//GameMap has items
private ArrayList<Item> itemsOnMap;

//GameMap has people
private ArrayList<Person> peopleOnMap;

//construct GameMap with rooms, items, and people
private GameMap(String mapName, ArrayList someRooms, ArrayList someItems, ArrayList somePeople)
    this.mapName = mapName;
    this.roomsOnMap = someRooms;
    this.itemsOnMap = someItems;
    this.peopleOnMap = somePeople;

public void addObject(Object o)
    if(o instanceof Room)
        roomsOnMap.add((Room) o);
    else if(o instanceof Item)
        itemsOnMap.add((Item) o);
    else if(o instanceof Person)
        peopleOnMap.add((Person) o);

Use overloaded methods:

void addObject(Room room) {

void addObject(Item item) {