Technically, "hadn't you?" is the proper tag question, but the "had better" form doesn't normally apply to tag questions. It's an odd piece of grammar. Replace "had better" with "should" and it'll sound natural.

Starting a sentence with "You had better...." sounds formal and/or British. An American would say, "The best thing to do is just smile and get on with it", or smile and carry on, is what a British person might say.

"We had better leave for the airport, hadn't we?"