This isn't the real name of the park (no one I asked seems to know it), but I've named it after the 'Retired Officials Activity Centre' (老干部活动中心 lǎogànbù huódòng zhōngxīn) next door.
In the afternoons it is usually buzzing with music performances of traditional local opera, ballroom dancing lessons, and games of Chinese chess or cards. There are masseuses, boiled egg sellers, newspaper vendors, as well as plenty of tables and chairs where you can sit, drink tea, and take it all in.
Here is a recording of some of the musicians performing in the park: