I want to smoke a goat
I'm Taiwanese. Asian markets are ok for goat, but your best bet is a Middle Eastern market or halal butcher for high quality, fresh goat. Halal butchers in particular are used to handling requests for whole goat or entire parts, and can usually get you what you need in a very reasonable amount of time. I actually had an instance where we were doing a pit-cooked whole goat, and I was able to get one the day after I ordered it.
My favorite local halal butcher is Wholesome Choice in Irvine, a large market which serves a predominantly Asian, Jewish, Middle Eastern, and Eastern European market base.
Wholesome Choice Market
18040 Culver Dr
Irvine, CA 92612
I would recommend the butcher at any one of the mexican grocery store chains around LA. You'll probably have to order in advance for a whole goat, but they might have goat parts readily available.
There are others, but I shop at this one (mostly because it's convenient):