To avoid calling .getName() twice I would use

name = city.getName();
if (name == null) name = "N/A";

You are opening lots of brackets { but not closing them where you need }.

I usually not just handing the code, but I've noticed you done must of the job, but confused where to close the brackets and a little bit at the program flow.

I only changed it a bit, there is a lot that you can cut and reuse code.

public static void main(String[] args){
    for(int i = 0; i < 4; i++) {

        System.out.println("Programmed by .");

        double standardCompact = 30.50;
        double couponCompact = ((30.50)-(30.50 * 0.07));
        double standardFullSize = 40.50;
        double couponFullSize = ((40.50)-(40.50 * 0.07));


        //Scanner Input
        Scanner input = new Scanner(System.in);
        System.out.print("Rent a Car? [Y or N]: ");

        //Response String
        String response = input.next().toUpperCase();

        if (response.equals("N")){
            System.out.println("You entered no. Bye. ");
        }
        else if (response.equals("Y")) {
            System.out.print("Compact or Full-Size? [C or F]: ");



            response = input.next().toUpperCase();
            if (response.equals("C")) {
                System.out.println("You selected Compact. ");

                //case1
                System.out.print("Have coupon? [Y or N]: ");
                response = input.next().toUpperCase();
                if (response.equals("N")) {
                    System.out.println("Price is" + " " + standardCompact + " " + "per     day.");
                }
                else if (response.equals("Y")) {
                    System.out.println("Price is" + " " + couponCompact + " " + "per day.");
                }

            }
            else if(response.equals("F")) {
                System.out.println("You have selected Full-Size. ");

                //case 2

                System.out.print("Have coupon? [Y or N]: ");
                response = input.next().toUpperCase();
                if (response.equals("N")) {
                    System.out.println("Price is" + " " + standardFullSize + " " +    "per day.");
                }
                else if (response.equals("Y")) {
                    System.out.println("Price is" + " " + couponFullSize + " " + "per day.");
                }
            }
        }
    }
}

You can extend this to any number of clauses, in perfect analogy to the if-else construct.

return a == b? "b"
     : a == c? "c"
     : a == d? "d"
     : "x";

In this form it quite closely resembles Lisp's cond, both in shape and in semantics.

But, do note that this is not a "shorthand for if/else" because it is an expression whereas if/else is a statement. It would be quite bad abuse of the ternary operator if the expressions had any side effects.

also I am not sure if 'else if' is supported in Java?

It is very much supported in Java as well.

if(day < 1 || day > 31) 
    this.day = 0;
else
    this.day = day;
}

If condition for day < 1 || day >31 cover's up everything, no need for else if, but you might need to consider for 30 days month as per your Business logic

else if(month = 2 && day > 28)
this.day = 0;

= is for assignment, and == is for comparison, Need to compare using ==,

 else if(month == 2 && day > 28)
    this.day = 0;