National Anthropology Museum
Even if you're not a museum person, like me, this is incredible.
You can spend a whole day there, or, if you'd generally rather stick forks in your eyes - here's the "must-do" plan.
Head to exhibition 5 to see the Teotihuacan artefacts, 7 for the Aztecs (also known as Mexicas) and 10 for the Mayans.
Also check out 8 for the Oaxacan Zapotecs if you're heading that way after Mexico City so you have the background.
They are all on the bottom level.
Then, head to A on level one for a comprehensive summary of all the contemporary indigenous cultures and skip the rest of the contemporary exhibits.
Of course, if you're into museums - then by all means do the whole lot - it's great.
If you'd like to know more about what you're seeing, you can hire a guide. Or just hover like a weirdo near the English-speaking guides talking to groups who paid.
Nearby Basque de Chapultepec is a huge parkland for Mexicans and tourists alike.
You probably spotted the huge expanse of green if you flew into the city.
As well as a zoo and two huge lakes with plenty of water activities, there's an awesome castle.
No moat sadly but it is perched high on a cliff with great views of the city.
Named grasshopper hill, it sits about 2300m above sea level and was once a sacred place for Aztecs.
But the grand building also has been used by military, imperials, presidents and is now a museum.
If you want to see how the other half lived in this city in the 1800s, this is the place.
Castillo de Chapultepec has a bazillion portraits of fancy schmancy looking noblemen, priests and their ladyfolk.
Plus there's a bunch of rooms with seemingly authentic representations of how they lived their life.
If you like stately buildings and pretty things, this is a real treat.
The jewellery, decor and other pristinely kept titbits are stunning.
I'd definitely live in that castle.
If you haven't got time for the anthropological museum, then Templo Mayor will give you a satisfying artefacts fix.
These ruins have seven layers of history as the Aztecs built new buildings over the top of the old to accommodate the expanding civilisation.
You can see key pieces and structures in situ just behind Mexico City's zocalo - the name of a city's central square across Mexico.
Some of the pieces, thanks to protection from the sun, even retain the original colours, albeit a little faded.
We're talking the 1300s to the 1500s. You know, a little while ago.
I initially walked past the museum within the grounds, in favour of exploring the other side of the ruins.
But I'm awfully glad guilt got the better of me.
Skip most of the bottom floor of the museo, except for the big tile in the centre, and head straight to level one where you'll find the contents of sacrifice boxes archeologists found at the site.
It's fascinating to see what pre-Hispanic cultures offered to the gods daily, believing it necessary for rain, food and wind among countless other things.
But as you weave your way up to the top floor and back down again, you'll see myriad other statues, masks, jewellery, art and tools found on the site.
After you finish at the temple, you can spend hours wandering around the zocalo and the cathedral - which has windows to some of the ruins beneath in front of the main doors.
The national palace, free on Sundays, can often have long lines and you need your passport to enter but you'll see some of Diego Rivera's famous murals if you make the effort to wait.
Then meander through the Centro Historico streets to gander some of the old buildings - snapping endless photos, of course.
Isabel la Catholica, 5 de Mayo, Franciso Madero and Simon Bolivar are among my favourites but any streets will do.
The Latinoamericana skyscraper, smog pending, has excellent views over the city and can give a great perspective of its size.
But the Revolution Monument, a bit further away, has great views too if you catch the lift to the top as the sun sets.
The fountains in front of the monument, with accompanying light show, make for great photos too.
Back in Centro Historico is Palacio de Belles Artes, a stunning building that puts our beloved QPAC to shame.
If you have time, the folkloric ballet - ranging from about $A90 to $A55 depending on the seats - is a bit of fun on Wednesday night, Sunday morning and Sunday evenings.
Apart from getting the chance to see inside a truly incredible theatre, complete with stain-glassed dome, there's folk dancing, traditional music, great costumes and comedy acts.
Just beyond the theatre is Alameda Park where you can people watch to your heart's content, especially good fodder on weekends.
This is the moment you'll wish you had your Fitbit with you if you decided to leave it at home.
So many steps.
But the reward is great, even if you don't have a watch to chart your progress.
The Temple of Quetzalcoatl - is actually one of three temples apparently.
Our guide told us robots have, in recent months, found tunnels that link all three.
A climb up some steep steps is rewarded with views of animals adorning the temples. Together with the pyramids of the sun, 239 steps to the top, and the moon they are UNESCO protected.
The authority says the city - believe to be occupied between 100BC and 500AD is "considered a model of urbanization and large-scale planning, which greatly influenced the conceptions of contemporary and subsequent cultures".
It's easy to catch a metro and then bus to the site, out of the city itself, but there are also plenty of companies offering tours.
Colour. So much colour.
How can you not smile while sitting on a pretty boat in a canal full of other party boats?
Especially when other boats connect to your boat to offer you tacos, and other delicious goodies, as well as flower crowns, souvenirs and music - from mariachi groups.
It's possible to do it yourself if you're in a group but if it's just you, jump on a tour.
And, no, it's not just for tourists.
On weekends, you'll see plenty of Mexican families taking the same trip on the water.
The agave worms were deep fried so they tasted a little like crisps.
The chapulines (grasshoppers) and hormiga chicatanas (ants) were also crunchy but you got that extra squish of their insides as you chomped.
While grasshoppers with guacamole and ricotta ain't half bad, I did not think I would be rushing back to munch on the crispy critters.
I was wrong, I've had them whenever offered.
Taco de maciza - beef head - should also be on the list at this market.
The guy literally grabs some cooked meat off a cow's head sitting on his table.
It will likely be the softest, melt-in-your-mouth, carne you'll eat.
La Merced market is not for the faint-hearted.
There's the odd smell that could send your stomach into a spin, they do like to display their animal parts prominently and you need your wits about you when it's busy.
But the reward is great - incredible food, dizzying sights and fun, to boot.
You know you're in the hipster area when you see a dog parking sign next to some hooks outside a supermarket.
This place has cute pastel-painted buildings everywhere you look but the real treasure lies in the bars and hole-in-the-wall eateries.
It's easy enough to wander around and discover the gems for yourself, just use Trip Advisor's "near me" function.
A good place to try Mezcal is Lavanderia, a former laundry happy to serve up the Mexican speciality.
If you discover Mezcal is not your thing - cough 'did someone say methylated spirits?' cough - it's right next to an excellent beer joint.
But for a guided tour, you can't go past Eat Mexico's late-night taco and mezcal tour through the area.
While every food on offer is worth raving about, the final one - served from a building that is a garage by day and taqueria by night - is worth saving a little room for.
HOT TIP: Water is not allowed into most museums or archaeological sites - make sure your bottle is empty before you enter.