Wow, I'm incredibly envious!!
Definitely miss Bloomingdales/Macy's...excellent description above.
Century 21 and Target are great for bargains - similar to TK Maxx.
Woodbury Common is an outlet village outside of the city which is good - you can catch a greyhound to it and also gives you a chance to see a bit of the suburbs. Maybe google to see if the brands on offer are of any interest?
Electrical is usually cheaper, if you're looking for anything.
Definitely incorporate tourist stuff with shopping, you won't care if you come home with nothing but you will care if you miss some of the sights. It's also a good way of coming across shops that you didn't know about.
Try and make it to a museum if you can, we went to MOMA and they had an amazing fashion exhibition on.
Central Park is lovely, I bet it's beautiful at the time of year.
Walk from Empire State all the way to battery park, you'll catch loads of sights.
Definitely go to Greenwich Village, great independent shops.
Don't bother with Statue of Liberty...
Enjoy!!!