I still visit the city every year to keep up to speed with life. I looked at the Harvard Club etc but they seemed rather expensive, particularly if you are solo.
February is a cheaper time to visit on account of the usual arctic conditions that apply. (You navigate around the city via shops or hallways that are warm!)
Try a webpage search for New York Budget hotels, only look at those in Mid-Manhattan and see what you come up with. You should find somewhere basic such as the Portland Square on 46th and 6th for around $130 a night.
I can make some other suggestions for very basic accommodations if you wish.
...but wrap up warm!