How do I correct my output of "available rooms"?

You are calling the display method on your Hotel object and that displays the Floors within that Hotel, but you never correctly initialized the Floor objects stored inside your Hotel object. Instead you created and initialized a separate Floor object (which is not connected to your Hotel).

If you want to initialize your Hotel's Floors, you need to loop over these Floors and initialize each of them separately.


P.S.: since you asked for more help, I modified the code to include the initialization. Most importantly, I changed the two classes to let you construct them as fully initialized objects. The most prominent changes are the introduction of a factory method for your Floor class and the addition of a loop in main() to construct the floors of your hotel:

#include<iostream>
#include<string>
#include <vector>
using namespace std;

class Floor {
private:
	int available_rooms;
public:
	Floor();
	Floor(const Floor& other_floor); // copy constructor - see below
	Floor& operator=(const Floor& other_floor); // copy assignment, see below
	static Floor make_floor_with_rooms(int number_of_rooms); // factory method - see below
	// getter and setter
	void set_available_rooms(int ar);
	int get_available_rooms();
	// utility functions
	void display();
};
class Hotel {
protected:
	string name;
	std::vector<Floor> floor_arr;
public:
	Hotel(const string& hotel_name); // Pass the name from outside, don't hide in implementation!
	void add_floor(const Floor& floor); // only add fully constructed Floor objects here
	void display();
};

Hotel::Hotel(const string& hotel_name) : name(hotel_name) {}
void Hotel::add_floor(const Floor& floor) {
    floor_arr.push_back(floor);
}
void Hotel::display() {
    auto floor_number = floor_arr.size(); // query number from floors vector
	cout << "The available floors are: " << floor_number << endl;
	int x;
	cout << "Select Floor" << endl;
	cin >> x;
	if (x < 1 || x > floor_number)
		cout << "Enter Valid Input" << endl;
	else
	    floor_arr[x-1].display(); // no switch statement needed
}

Floor::Floor() {
	available_rooms = 0;
}
Floor::Floor(const Floor& other_floor) { // copy constructor - see below
    // this is required to use the container class, std::vector
    available_rooms = other_floor.available_rooms;
}
Floor& Floor::operator=(const Floor& other_floor) { // copy assignment, see below
    // this is required to use the container class, std::vector
    available_rooms = other_floor.available_rooms;
    return *this;
}
Floor Floor::make_floor_with_rooms(int number_of_rooms) {
    // this is a helper function to create a Floor object that is fully initialized
    // this is a good way to make sure that you don't construct invalid objects
    Floor new_floor; // default constructor sets rooms to 0
    new_floor.set_available_rooms(number_of_rooms);
    return new_floor; // now we have a fully initialized object
}
void Floor::set_available_rooms(int ar) {
	available_rooms = ar;
}
int Floor::get_available_rooms() {
	return available_rooms;
}
void Floor::display() {
	cout << "The available rooms are " << available_rooms << endl;//output is 0
}

int main() {
	int a, b;

	Hotel my_hotel("Hotel California"); // create an initialized hotel object

	cout << "Enter available floors" << endl;
	cin >> a;
	
	// now iterate over the requested number of floors to create and initialize them
	for (int i = 0; i < a; ++i) {
	    cout << "Floor " << i+1 << ". "; // add a little information to guide the input
    	cout << "Enter available rooms" << endl;
    	cin >> b;
    	// now create an initialized Floor object with the required number of rooms
	    my_hotel.add_floor(Floor::make_floor_with_rooms(b));
	}

	my_hotel.display();

	return 0;
}