Hi Percy, welcome to the forum.
How are they organised?
There’s less to distinguish areas of Chengdu compared to areas of a place like Manhattan, but Chengdu is informally divided into quadrants and and officially into large districts (like 武侯，高新，金牛, etc). Those districts are so large they barely serve to define anything, though. Within them are neighborhoods (like 玉林，桐梓林) which are more of what you’re looking for: descriptors of what local life is like, in a neighborhood sense.
Hopefully this is helpful to you. Check out Chengdu Places which has locations in the city organized by quadrant, you can browse around and see what’s in Chengdu. Aside from browsing by city quadrant, there is a listing of places specifically in the Yulin neighborhood, which is in the Southwest of Chengdu.