This link indicates the United Parcel Service (UPS) observes New Year's Eve as a UPS holiday, with only delivery of air and international packages. For New Year's Day, another UPS holiday, they will only deliver parcels sent using UPS Express Critical service.

UPS Next Day Air Early A.M.

UPS Next Day Air

UPS Next Day Air Saver

UPS 2nd Day Air A.M.

UPS 2nd Day Air

http://www.ups.com/content/us/en/resourc...

Wed, 12/31 is a normal business day

Depends on the city. Call your local branch and ask.

no deliveries on NY eve except air and international pkgs