I haven’t made it to Manchu Picchu yet, but as an Old World archaeology enthusiast, I visited some Mayan sites in the past year and was way more impressed than I expected to be. If you think like I used to & and assume that all the cool old stuff is in the Old World, consider challenging that assumption :)
Calakmul in Mexico was my favorite. I loved climbing the steps of a pyramid, rising above the jungle canopy, and then seeing a pyramid twice as high staring back at me.
I can't recommend Calakmul enough. It is a far larger and more interesting site than Chichen Itza, by a substantial margin. And, there are at most a few hundred visitors per day (we saw maybe ~100 total the day we visited) vs 6000+ per day at Chichen Itza. You can climb all the structures at Calakmul and the understanding you get of the scope, views of the rest of the site and surrounding area, etc are incredible.
Here are a few pictures I took at Calakmul of two of the many large structures:
The "Mayan Train" is currently under construction and may eventually bring many more tourists to the area - I would highly suggest going before that happens and everything there changes. (It will be great for the region in terms of economic impact, but the status quo with few visitors on incredible sites is really magnificent.)
The ruins at Becan, Xpuhil (Xpujil), and Coba are all also really incredible - and only a handful of people visit them per day. You can easily stay in Bacalar, visit Chetumal in the morning, drive to see Becan and Xpujil in the afternoon, and then visit Calakmul the next day. (Driving back to Tulum/Playa del Carmen/etc makes for a long drive afterwards, but is certainly doable.)
Fly into Cancun, rent a car, and then go drive down the coast and plan various stops for a really great trip. Playa del Carmen and Tulum are fun, of course, in an "international tourism" sense. Bacalar and Chetumal are also "tourist towns", but they are very different - think of a small, charming beach/lake town with an older, more original/authentic feel.
Prepay for the rental car, too. If you prepay, you'll get the agreed upon price. If you don't, you may find your rental car doubles or triples in price. Best to book on the rental car's website.
From the top of one of the tall structures in Calakmul, you should be able to see El Mirador on a clear day, possibly with binoculars. El Mirador is on the Guatemalan side and is also a pretty amazing site, especially if you want to see what some of these sites look like before they are fully excavated and cleaned up for tourist crowds. El Mirador is deep in the jungle and requires a multi-day journey, preferably with mules to get there. When I went several years ago, I remember only crossing paths with one other group of tourists for the whole 60 mile round trip journey.
I recommend the region, and just getting yourself or a small group into the area and going to smaller sites.
Machu Picchu is impressive. However it is overwhelmed by tourists and the modern structure in the valley below detract from it.
The small sites on the various trails in are quiet, and incredible. Many haven’t been reconstructed is dubious fashion. It’s am amazing area.
Calakmul in Mexico was my favorite. I loved climbing the steps of a pyramid, rising above the jungle canopy, and then seeing a pyramid twice as high staring back at me.
https://en.wikipedia.org/wiki/Calakmul