Roma Norte: Roma Norte is the center of Mexico City's culinary and artistic scene. Its central avenue, Avenida Álvaro Obregón, is lined with eateries and sidewalk bars. Mercado Roma is a great spot for international food stalls.
Condesa: Condesa is known as a hipster neighborhood with a relaxed vibe, art galleries, green spaces, artisan boutiques, and trendy restaurants.
Polanco: Avenida Presidente Masaryk is the main shopping avenue, filled with world-famous brands and upscale restaurants. Side streets host Spanish Colonial Revival mansions.
Other beautiful neighborhoods: Reforma, San Angel, Coyoacan.
Frida Kahlo's childhood home, and the home that she later shared with husband Diego Rivera. You can pair this with a visit to the Coyoacan neighborhood (just a quick walk from the museum). Advance tickets necessary.
Lovely park in the heart of Condesa, surrounded by two ring roads full of great shops and food. Worth an early morning walk.
The main square in CDMX and a great spot to take in. Visit the Cathedral, and be sure to go in the Zocalo where you can see many of Diego Rivera's most prominent paintings and frescoes for free.
Containing nine museums, a zoo and Chapultepec Castle, you could spend your entire day walking around this beautiful park.
Incredible pre-Aztec pyramids! Stop for breakfast or lunch in the local town, and then finish off by touring the pyramid grounds by foot.
San Juan Market (food) and Mercado de Artesanías (gifts/textiles/trinkets) are basically side by side. These two markets are great for local produce, spices, and houseware.