Henan awaits:
Kaifeng is a laid-back town about 90 minutes to the east of Zhengzhou. Enjoy ancient temples and an escape from Chinese skyscrapers. Kaifeng was the capital of several dynasties before it slid into irrelevance the last 200 years.
Another great city nearby by is Luoyang, home to the Longmen Grottoes. The city itself is worth a look, with an interesting old section and easy walking downtown. It's about three hours by bus, which leave Zhengzhou every hour or so. An express - the "elephant bus" or kuai che - costs ¥40.
Yuzhou is a small and relatively undeveloped city, off the main rail network, but well worth a visit to see the Jun Royal Kiln Museum and to get an insight into life in Henan off the tourist trail. One and a half hours by bus, and very walkable once you get there.