Can anyone recommend of a nice hotel to stay close to Zhengzhou downtown , near shopping mall , restaurants etc... ? ( and not too far from AIRPORT )

As I know, the airport is around 30km from the city center, so it may a little hard to find a hotel concerning all your requirements. Anyway, I recommend the local Golden Sunshine Hotel to you. It is near the local Railway Station and the restaurant and shopping malls are available nearby. To airport, you can easily find the shuttle bus at West Square of the Railway Station.