Removing First and Last Double Quotes

If the " characters are always going to be the first and last ones, you don't need a regex. Just use substring:

x = x.substring(1, x.length() - 1)

try this regex

s = s.replaceAll("\"(.+)\"", "$1");

Try this code:

public class Example {
    public static void main(String[] args) {
        String x = "\"‘Gravity’ tops the box office for 3rd week  | New York Post\"";
        String string = x.replaceAll("^\"|\"$", "");

        System.out.println(string);     
    }
}   

it gives:

‘Gravity’ tops the box office for 3rd week  | New York Post