What better way is there of leaving a country than turning up at the airport, bags in hand and asking for the next available flight out of the country? Of course, the danger is that you just missed the last flight for a week, but if you can't go where you want to go, you can always choose somewhere else interesting.
Fortunately for me, I knew when the flights left and just had to follow my hunch that there would be seats available. I really do recommend doing a runner at some point in your life. It is very liberating!