Beckles,
Based on my reading of their terms and conditions, I think you DO qualify for multiple eligible stays by checking in and out at different Starwood hotels in the same city (e.g. NYC in Catman's scenario).
Below is from terms and conditions of the Starwood's Preferred Guest Program:
"An "Eligible Stay" is defined as one or more consecutive nights spent at the same hotel, whether or not you checked out and checked back in again, during which you paid a qualifying room rate and a Preferred Guest membership number is presented at time of registration."