I haven't stayed at Windsor Court, but I've had dinner there. It's about a 5 minute or so walk from there to Bourbon Street. The Riverwalk and casino are both closer, just a couple of blocks away. The hotel looks to be extremely nice, and the restaurant was fabulous.
The only criticism I would have is that it doesn't "feel" like you're in New Orleans when you're inside its walls. But that can be a positive, too. New Orleans is all around you, of course, and it's nice to have a refuge in the heart of all the action.
All of this is from memory, and this was my big birthday trip so it's possible the details are a little fuzzy. In fact, I was pretty fuzzy myself by the end of the trip.