Tlalpan Centro
Extremely popular with Mexican families, especially as a place to stroll and people-watch on weekends, this historic and enchanting historic center laid out in the 1600s is sometimes described as what Coyoacán felt and looked like 30 years ago, before it became more of a must-see destination. Slowly but surely, Tlalpan's narrow lanes of colorful, historic houses and its charming tree-shaded hub, Plaza de la Constitución, are drawing more sizable crowds, but a visit here still feels manageable and relaxed, like you've stumbled upon a small colonial village far from the big city.
Do visit the Capilla de las Capuchinas, a few blocks away, to admire the strikingly modernist interior, which Luis Barragán completely redesigned in the late 1950s. You can also walk through the courtyard and view the interior of the imposing Parroquia de San Agustín de las Cuevas, on the east side of the plaza. Next door are a couple of good quick stops for a refreshment: historic La Jalisciense cantina for Spanish food and tortas, and an atmospheric branch of the local ice-cream chain, La Nueva Michoacana (which has been going strong since the early 1950s). If you can visit on a Sunday, you can enjoy watching locals, many of them seniors, dancing around the grand kiosco in the Plaza. Vendors sell crafts, souvenirs, and food while just a few steps south, Mercado de la Paz is a traditional market that also has plenty of food vendors. And although Tlalpan isn't flashy as a dining destination, there are a number of mostly traditional restaurants, cantinas, and food vendors on the blocks around the plaza, especially along pedestrianized Calle Guadalupe Victoria (which extends south from the plaza western's edge). Along here you'll also find the quirky but excellent Museo del Tiempo Tlalpan and the Museo de Historia de Tlalpan that, while not a must, offers free admission and gives a good overview of the neighborhood's history.
Finally, on the north side of the Plaza, the performance venue Multiforo Tlalpan often has concerts and other interesting shows—it's worth checking to see what's on. Tlalpan is in the south, easily visited in conjunction with Xochimilco, and most conveniently via Uber. But you could also save some pesos by taking the Metro to Universidad or the light rail to Huipulco, and taking much shorter Uber rides from either. Or you can take the Insurgentes Metrobus line south to the Fuentes Brotantes stop in Tlalpan Centro.