travel from ZhengZhou University

1. Do you mean the Baiyun Mountain in Luoyang City? If yes, you may walk 600 meters along Science Avenue to Zhengzhou University Metro Station first. Then you may take metro line 1 to Wuyi Park Station, Exit D. Then you may walk 20 meters ahead to Tongbai Road Jianshe Road Bus Stop and take bus no.b1 to Zhengzhou Bus Terminal. Then you can catch a long distance bus to Baiyun Mountain directly. This bus departs at 12:50 and 16:20. The ticket fare is 72/person. You are advised to take 2 days to visit this mountain.
2. Shaolin Temple: You may walk 200 meters along Science Avenue to Zhengdaxinqu South Gate Bus Stop and take bus no.b12 to Railway Station Bus Stop. Afterwards, you need to walk about 170 meters to Zhengzhou Central Bus Station and catch a long distance bus to Shaolin Temple directly. This bus departs at 07:00, 08:00, 08:50, 09:40, 10:00 and 11:00. The ticket fare is CNY48/person. You can just spend one day there.
3. Kaifeng: You may walk to Zhengdaxinqu South Gate Bus Stop and take bus no.b12 to Railway Station Bus Stop. Then you may head for Zhengzhou Central Bus Station and catch a long distance bus to Kaifeng directly. This bus operates during 07:30 and 19:00. The ticket fare is CNY18/person. You are advised to stay there for around 3 days.
4. Huanghe Scenic Spot: You may walk 130 meters from North Gate of the university to Lianhua Street Shixinzhuang Bus Stop and take bus no.271 to Guxu Road Dahe Road Bus Stop. Then you may go across the road to take bus no.723 to Dahe Road Jiangshan Road Bus Stop. After that, you may walk 260 meters backwards and take bus no.18 to Huanghe Scenic Spot directly. You may stay there for half a day.
Have a nice trip!

Thank you so very much for the detailed and informative response!!

I see that the ride from Zhengzhou university to the railway station is around 2 hours!
is there any other way possible to get there? by metro maybe?
and do you maybe know when the last bus is leaving Shaolin Temple?

Thanks!!