This lovely museum is near our home. I go as often as possible on Tuesdays (free day!) to enjoy the cafe and watch the peacocks. It's a real hidden gem.
The famous pyramids are about a 2 hour drive away, but absolutely worth the day trip. There is a museum/gift shop, another museum, and of course large grounds to walk around and climb the pyramids. There is also a restaurant near or on the park grounds. I announced to my parents that David and I were dating by sending them a selfie of us kissing on the top of the Pyramid of the Sun. If you're looking for a way to get there, we can help you find a driver or a ride.
This museum absolutely blew my mind. It's always free, and a great way to spend most of a day.
Chapultapec is a huge city park/forest in the middle of Mexico City. Entrance to the park is free, and there are lots of vendors selling food, clothes, and just about everything (though this is not an artisan market). If you're going to visit Chapultapec, expect to make a day of it. CASTLE: The castle is the castle of a Hapsburg royalty that Napoleon tried to instal here in Mexico (spoiler alert, it didn't go well...) I loved the tour of this castle, it is stunningly gorgeous and a great museum. ANTHROPOLOGY MUSEUM: This is an internationally-known museum. I've only visited briefly, but in itself could be a day's outing. Entrance is about $5usd/ person. MODERN ART MUSEUM: I have not visited, but it is also well-known