I'm not MFNYC but can offer a few suggestions for parking. First, go to iconparking.com, a website that has a network of parking lots across the city. You can plug in your dates, a location and see what's available and what it will cost. You can even make a reservation!

Another option is the multi-level garage on 42nd st I think between 8th & 9th. It's self serve though. You park and lock.

There may be some other options in previous threads if you try a text search parking AND nyc.