Rates are enormously variable in NYC. Right now things are pretty quiet and there are tons of good hotels available for $200 or less (my parents had a very spacious high floor king room with a view of Central Park at Le Parker Meridien this week for $249). At busier times of year it's hard to find anything remotely decent for under $350/night, and at peak times it can be hard to find a room at all for under $400-500.

Another suggestion would be the NoMad. They have rooms with big clawfoot tubs that fit two people. It's not a jacuzzi (no jets) but a comfy bathing experience.