If you're not into the relaxing on a beach thing, I would have to say the two most memorable trips I have ever taken would be China/Japan and Israel/Egypt. We did these in 3 week so we could give each country about 10 days. China would probably be my recommendation. The great wall, the forbidden city, the art, and the food. It is absolutely unforgettable.
I will add one caveat: my trip was over 12 years ago and our tour guide took us around in Mao's old limousine (I Really don't know how we arranged that) so things might be different these days.