Hey Nato,
Chengdu has (in my opinion, and limited ecperience) the best expat culture scene outside of BJ and SH, and it all centers around Cafe en Seine. It's a hipstery/trendy/artistic/funky and certainly decadent scene, whether or not that appeals to you.
Otherwise, there's the English pub (The Leg and Whistle) just down the road which is well-stocked, friendly and a lot less pretentious, though as you can imagine, the two circles overlap a lot.
I had a BALL in Chengdu, you are making a great choice teaching for Chuan Da. And trust me, 4000 is a comfortable living wage in Chengdu, I never spent it all, and you'll have plenty of time for moonlighting.
Best of luck!