One good option is to go to the bars at El Rodeo or Las Haciendas restaurants for a few drinks, particularly when they have live music (frequently on weekends).
Two other good spots for a drink are Antigua Hacienda (from 10 a.m. daily), 1.5 blocks from the parque, facing El Rodeo and Cuates (from 10 a.m. daily), serving up Mexican comida with its beers.
Zotz, two blocks from the parque, is a slightly yuppified bar with a convivial atmosphere and the best mix drinks in town. Open late.