I will be in New york next week for 10 days and I'm wondering where I could find some cool cheap used analog stuff? (Mics, preamps...)
I assume that you mean New York City (not the state)...
I don't live in the city, but even if I did I would not know for sure, maybe with exceptions of few places. ... maybe
Also depending which part of the city you are going... that place is pretty big and traveling within it, finding places etc ...hmmmmmmm? , how should I put it??? ... - good luck

as I always say : the good part is, that the food is good pretty much everywhere in the city
I would imagine, what you could do would be: when you are there ... get the local directory/phone book and look for various musical instrumets and equipment stores... or get on-line and do search that way, and see for yourself. See the stores descriptions if they sell used stuff (most of musical instruments/gear stores do). You never know what you may find there in used gear section/corner... ..Or just give them a phone call and ask if they have some analog gear at the moment (or specifically about something you are looking for) ... simple as that.
Also, asking people on the street will not going to help you much if at all, but it may be a "fun experience"
I've tried to search something... you get the whole list of places... which I have never been so have no idea.
HERE is the link , which I'm not sure if it will work on the b-board. I've started the search
HERE
..have a good time in the city.
/respects