I don't think it really matters. When it comes to the numbered
streets, people seem to typically say the street first: "102nd
Street and Broadway," or "68th Street and 3rd Avenue." But when you
get below the numbered streets, I don't think it really matters.
Someone is just as likely to say, "2nd Avenue and Houston Street,"
as, "Houston Street and 2nd Avenue."
When you get below Houston Street, there aren't that many wide
avenues. The streets down there are all very tiny, and they run in
crazy zig-zags. The neat grid pattern that Manhattan is laid out on
disappears below Houston Street. The majority of the avenues below
Houston are actually called streets, such as Centre Street, Varick
Street, Hudson Street, etc. Centre, Varick and Hudson Streets run
south/north, not east/west, so technically they are avenues, but
they're called streets because they're small, and because they
don't run in straight lines.
Related Q&A：
Do you say the street or avenue first in Manhattan？-Well, in Manhattan, usually you say the avenue first. For example, if it's 5th Avenue and 42nd Street, you'd mention 5th Avenue before 42nd Street. But it's not a hard and fast rule. Sometimes people might just say it in the order that comes to mind or depending on the context. It can vary a bit depending on the person and the situation. But generally, the avenue gets mentioned first. Oh, and don't forget that Manhattan's street and avenue system can be a bit confusing for newcomers!
