I had really bad skin in high-school and college. Unfortunately, my parents had me take antibiotics for years instead of just going through with a treatment of Acutaine. To be frank, I'm stunned that I don't have more severe acne scarring, fortunately my minor scarring is covered entirely by my beard.
In my last two years of college or so my skin started to improve but was still incredibly dry and I continued to have dark circles under my eyes (which I've pretty much had permanently since childhood).
I stopped drinking as often for about a year prior to completely stopping drinking, so I'm not sure how useful my experience will be to you, however I'd say about 4 months in I really started to notice how vibrant my skin was. Zits would clear within 1-3 days and my skin seemed to need less moisturizer and have a healthy "oily" texture.
As someone who used to really enjoy drinking, I have no clue how or why people keep up drinking habits just to bend to social "norms".