On a separate note, a certain luxury hotel in New York offers long-stay monthly (30 days at a time) rates in their top suites at what would be equivalent to roughly 10 nights rack rate. These are suites that typically have very low occupancy. Your monthly rate would be roughly USD 6-figures.
Also, in some jurisdictions, if you stay for more than 30 days, certain city/local/state etc taxes (the kind of taxes geared towards short stays) are exempt.