If you were to seek advice on what stops to make on your world tour, you may consider talking to a journalist.
We're the experts; the ones paid to explore the furthest reaches of the globe.
Anthony Lobaido chronicled some of his journies in the article "The world's best destinations."
Credit given where due he didn't rattle off the Great Pyramids, ancient Mayan temples (though a Mayan city was mentioned) or the Grand Canyon.
His list included Victoria Falls in Zambia as well as the neighboring Chobe Game Reserve which has the largest population of elephants in the world.
Other suggestions include an island off the coast of Belieze, followed by a stop to the aforementioned Mayan city in Guatemala.
You may even consider becoming a monk in Thailand for a day. According to the article you can become a monk for as long as you want.
Personally, if you want an off-the-beaten path site, check out the Church of St. Peter & St. Paul in Chaldon, Surrey, UK. Many world travelers I've met in my day feel they've seen fifteen churches, they've seen them all. Frankly, I'm usually inclined to agree. This one, on the other hand is on the opposite end of the spectrum from your Notre Dames, Canterburies and the lot of the world's cathedrals. This obscure little brick hut about fifty-foot square and located more or less in the middle of a field on the very southern edge of what is today greater London.
What makes this hut-like church significant is that it happens to be mentioned in William the Conquerer's Domesday Book. That book was created around 1100. The mural on the back wall is believed to have been painted sometime between 1170 and 1200 by a monk living there at the time.
Even a trip to an unassuming bar in Mojave, California is worth a trip, especially if you're an "air-head." The bar - aptly named A Wing & A Prayer - is covered in aviation memorabilia. It isn't quite the old Ranch that the Edward's test pilots of Tom Wolffe's "The Right Stuff" fame, but it certainly is worth a visit. If you leave time you might be able to sneak out up to Edwards Air Force Base and have a shot at scavangering some bits of aviation history yourself. The desert around the base is littered with bits of almost seventy years years of the most famous aircraft.