Machu Picchu, Peru
More exactly, the destination is that of the Incan ruins, which you actually have to take a bit of a hike to get to. The Peruvian coast is always affordable and the Incan trail is sure to be an adventure. Once you get to the ruins the view and the sights are amazing. Don't forget your camera.
On the coast of the Black Sea, Varna is one of the most affordable resort towns in eastern Europe. While you are there check out the "Gold of Varna" exhibit at the Archaeological Museum. The 6,000 year old jewels were found in a necropolis, and quite a sight for any budget minded treasure seeker.