Parque México. Casa Lamm. Street food. Art galleries. Shopping. Bars. Restaurants. Head to Calle Colima and explore. If you head west you'll hit the neighborhood of La Condesa. Make your way to Parque Chapultepec while you're there. If you have time, go about an hour south to Coyoacan and visit La Casa Azul (Frida Kahlo's historic house), Coyoacán Market, and Jardín Centenario.
Spend some time walking around Zócalo, (the historic square), but we wouldn't suggest doing this on Saturday! It gets PACKED and you might be stuck in a sea of people for a few hours trying to get in and out. Also check out the Palace of Fine Arts and Museo Nacional de Antropología if you like museums.
Dinner Friday night will by in Polanco (~20 minutes from Roma Norte), so you have the option to spend your Friday afternoon here and meet at the restaurant for the welcome dinner (just keep attire in mind). If you make your way here, we highly suggest visiting Chapultepec Park, one of the largest city parks in the world. It has a zoo, museums, and a castle! Museo Soumaya is great for those looking for a museum, and Avenida Presidente Masaryk has luxury shopping and dining if ya fancy.
This one is best for a group. Another half day adventure about 40 minutes outside the city, but worth it if you have the time! Gondola-like boats take visitors on cruises around the canals while food vendors, artisans and mariachi bands float past. If someone floats by offering to make you quesadillas, we highly suggest you take them up on it. Another museum suggestion: Dolores Olmedo Museum
Mexican wrestling! Either at Arena Coliseo or Arena México, this is a must if you'll be in town on Tuesday or Sunday. Unfortunately they only have matches on Tuesdays and the weekend.
It'll take about half a day to set aside time to visit the ruins, but if you're willing to travel about an hour outside the city, it's worth it. If you'd like to eat lunch in the area, head to La Gruta Restaurant, built inside a natural volcanic cave (the food isn't fantastic, but the atmosphere is very cool).
About 30 minutes from Roma Norte, it was home to Frida Kahlo and Diego Rivera (now a museum). A great place if you're looking for arts & crafts markets. Check out San Ángel Saturday Bazaar and Bazar Sábado.