It's going to take you three days just to get over the jet lag from the flight to the opposite side of the world.

Have you considered Argentina? Minimal jet lag, Buenos Aires is beautiful, almost like Paris, and best if all, stupid cheap.

As a bonus, you can catch a ferry across the river Plata and go spend a day in Uruguay, either Colonia or even Montevideo. Two passport stamps for the price of one!

Santiago comes to mind as well. Lovely city, bit more expensive but still pretty cheap.

Or how about Central America? Costa Rica, Belize, Panama...

Bottom line, you have a very limited amount of free time; recuperating from the flight alone will eat up most of it.

If you had two weeks on the other hand...