By train,
Chengdu do not have direct trains to Yantai, you should make a tansit in Jinan. It is quite a long jurney, perhaps 35 hours plus 7 hours.
Nanjing has one train No.2582 to Yantai, which take 16 hours from 2:41 to 18:39. Fare: about 250RMB for hard sleeper Train 2582 depart from Shanghai and passes Suzhou, Wuxi and then Nanjing to Yantai. Takes about 18 hours from Suzhou and Wuxi to yantai, nearly 20 hours from Shanghai to Yantai.
For flights:
you can use this:
www.travelchinaguide.com/china-flights/