We do fairly frequently (although not in NYC), usually to save money. Once, absolutely. I might hesitate at twice.

Yep. Would do it and have done it. One trip I was at the LaQuinta on points and switched to the Hilton for a Priceline room. It's not a problem at all. That trip also confirmed I prefer the convenience of a mid-point hotel (free wifi, breakfast, access to business club and free printing of theatre tickets) vs having to pay for everything at a "nicer" hotel.

I actually think it would be quite a bit easier to do this in NY than elsewhere because Manhattan is so compact. True you'll go 3 or 4 hours without a room, but leaving one hotel and getting to and checking into the other shouldn't take more than a couple of hours at most.

Thanks for all the responses--lots to think about here! Unfortunately, I don't think we will be able to get all six nights free no matter what we do, which is fine. And I love and have used Quikbook, Travelzoo and Priceline, all of which offer lots of low-cost options in New York. And I am considering staying in a more "neighborhood-y" type area rather than the tourist center. For those familiar with maitaitom's recent trip report, The Chelsea Pines Inn might be a fun option as well.