There's relatively few things to do in Zhengzhou but a possible evening might involve eating at a Sichuan or Henanese restaurant, buying yourself a bottle of decent Dynasty wine, parleying with the local clentele, getting lazy, and rounding off the evening at a KTV bar.
Museum Area
One thing worth knowing about is that the museum area is also the area of the 2 branches of government - federal and communist - so the area is much nicer. We are talking trees and some flowers along with a more neighborhood feel that might remind you of Shanghai. Do not expect wild nightclubs, but it is a more pleasant place to be if you are looking for a walk. Erqilou is fine, but a bit dirty, so see this other side of Zhengzhou if you get a chance. Also, some nice places to eat are in this area.