We had plans to do this same thing, but it's supposed to rain and I'm not in the mood to get soaked (have been rained on my last 2 trips to NYC. Not doing it again)
Anyway.... Maybe start at Union Square (14th st) and head south on Broadway. You'll be getting into SoHo. Some fun shopping there, but it can get expensive. From Broadway, you can turn right (head west) around 8th or Bleeker or something to be in the Village. Some fun stores and restaraunts there.
For some real funkiness, turn
left from Broadway (east) onto 8th St. This becomes St. Marks Place after 3rd ave, I think. Fun second hand shop called "Search and Destroy."

Cool street vendors there too (if it doesn't rain!).
Chinatown gets on my nerves lately ("handbag, handbag, handbag!" and lots of junk) But I love eating in Little Italy. Not sure there is much shopping there.
Wishing you sunny skies. My plans are still up in the air, but you should have fun!
I