Many hotels offer day trips out to Philadelphia and it's mslls/outlets and other places where sales tax is lower and prices are not geared for the tourist market. These are worth a go.
Other places to try for dirt cheap trainers are the shoe store that is part of Century 21, near to ground zero. It is part of the store, but accessed from a side street (head towards McDonalds). From there I got a pair of diesel trainers for $39, when in the UK the best price I have seen is �50.
Also, try, the area near canal street (walk there from century 21, in the uptown direction) are also good. Here you will find many cheap trainers (amongst other things), not all of them legit! I wouldn't go there after dark though.
There are lots of little shops in Greenwich village that sell great shoes and clothes, though not cheap, they have a fantastic range and choice. Go to sixth ave where it meets Bleecker and start there. This area caters for the university AND the trendy crowds.
Finally, don't do a Colleen! Wear your products at least once and ditch the boxes before you return, otherwise the taxman will want a bit!