I second the suggestions made by Balthisar and susan. Uber works very well and is very affordable.
Keep in mind that it takes a while to get from one point to another, even if the distances do not appear that great on a map.
If you plan to go to Teotihuacan to see the pyramids, plan for a whole day. Xochimilco can also take a while to get to from downtown, but the *trajineras * are well worth it.
Just the area around el Zócalo/ Palacio de Bellas Artes can easily keep you busy for the weekend. If you go to el Zócalo, take a look at the Templo Mayor Museum, next to the Cathedral.
In the Alameda, next to the Palacio the Bellas Artes, is Museo de la Estampa (contemporary printmaking museum, https://museonacionaldelaestampa.inba.gob.mx) and Franz Mayer Museum (decorative arts from renaissance to the present day; http://www.franzmayer.org.mx.)
The National Museum of Art is across the street from Bellas Artes. In the corner of the museum is a restaurant called Los Girasoles (http://restaurantelosgirasoles.com.mx/contacto1.html).
The food is good, it is a good place to try some exotic dishes like escamoles or tacos de chapulin.The opening of the most recent James Bond movie was filmed in that area.
Museo del Estanquillo. (http://www.museodelestanquillo.cdmx.gob.mx). is within walking distance from el Zócalo, and generally has good exhibits.
Coyoacán, where Frida Kahlo and Diego Rivera´s house (La Casa Azul) is, is also very nice. Café el Jarocho is a nice coffee shop chain there.
Colonia Roma and Colonia Condesa are nice if you want to see contemporary art galleries, both areas have good restaurants, coffee shops and night life, especially la Condesa.
The Museum of Anthropology is definitely a must see. I particularly recommend the Aztec room, where the Aztec Calendar and the Coatlicue are. Across the street is the Modern Art Museum, and next to it is Rufino Tamayo Museum, which caters toward young contemporary artists.
Food wise, Rosetta (http://www.rosetta.com.mx), both the restaurant and the panaderia, are quite yummy. Just be sure to make a reservation, because they get very crowded. Both are in Colonia Roma.
If you like sushi, Kyo Sushi (http://www.edokobayashi.com/sushikyo.html) is awesome.
If you happen to be in Colonia Roma by night and you are looking for street food, you might want to check out a taco stand right in the corner of Álvaro Obregón and Insurgentes, called “El Gato Volador” (The Flying Cat). It is just a tiny stand in the sidewalk, but the tacos are to die for.
La Opera (http://www.barlaopera.com) is a traditional cantina/restaurant near El Zocalo, where you can see a hole in the roof that local legend says was made by Pancho Villa.
Café de Tacuba (http://www.cafedetacuba.com.mx/en/) is a nice café/restaurant also within walking distance from El Zocalo. The café lechero and the tamales oaxaqueños are very good.
Mexico City is a great place, I hope you and your friends have a great time!!