strangely enough I was just pricing car rental a few min ago for the same set up, staying midtown going to woodbury.... So far both Enterprise and dollar were coming in around $60 for a days rental (8am to 7:30am next day).... As yet I hadn't read the small print regarding all the crash damage waiver, etc that always manages to add on a few more quid! Also as car is coming back next day (so far office I've checked have closed at 7pm, and I estimate i could still be in transit), is a nights parking would around $30-35 depending on exactly where we go.
But something to keep in mind is that most of the shopping outlets do have a central locker area so you can rent one and offload your bags during the day.