The real reason to stay at the Algonquin is history. Heck, I got upgraded to the James Dean suite and it is kind of cool to think he actually stayed here. The other rooms I've stayed in are very tiny, but they have this zillion dollar bed which is terrific.
The furnishings are very nice and they have an amazing jazz bar which of course I've never been to.
The health facility is just a tiny room with weights and the bathrooms are tiny and not very nice.
This place is very expensive, so try expedia.com to try to get a better deal.
The location in midtown is awesome. You can also try the similar Sofitel next door or the Royalton across the street.