Tipsy,
Call Air Pegasus: (212) 563-4442
That's the West 30th heliport.
Don't have exact landing fees but I understand it's north of $150 per contact. No overnight parking. Jet-A is available.
Downtown Manhattan Heliport is crowded with tourist tour traffic. All of the tours use this heliport.
East 34th St is small and closed on the weekends.
If you're open to a non-Manhattan heliport, check out HHI (Kearny).
HHI Heliport . Quick drive into Manhattan, large hangar, maintenance base.