Take your passport with you when you go to Macys' and Bloomingdales. If you visit the customer services desk and show them your nationality you get a free gift (branded holdall bag, keyring, beach towel) and a 15% store discount card.
Duane Reade (SP) the pharmacy has really cheap skincare and perfumes.
Greenwich village has loads of little boutique style shops with really unique items in them and wandering round the area for a day is great fun.
Harry's Bar down in Wall St is a fantastic steakhouse. The cocktails are amazing.
Bar 89 - I think it is on mercer, check out the toilets!
If you are there at the weekend go for Brunch at the Ritz-Carlton down near battery park. The food was delicious and you are overlooking the statue of liberty. I was lucky enough to see Mr Big of SATC fame when I was there.
Have fun.