The following holidays ONLY as far as NYC DOT is concerned are "major" legal holidays: Jan. 1, Memorial Day, July 4, Labor Day, Thanksgiving Day, Dec. 25.
On those 6 days, unless parking is restricted 7 days a week, parking is permitted anywhere (metered parking is also suspended). [Of course parking at hydrants is NEVER permitted.]
Various media NY Times, WCBS etc. only note "alternate side of the street is suspended"--they should be more accurate.

From NYC DOT:
On major legal holidays, stopping, standing and parking are permitted except in areas where stopping, standing and parking rules are in effect seven days a week (e.g., “No Standing Anytime”). Parking meter regulations are also suspended on major legal holidays. The major legal holidays are New Years Day, Memorial Day, Independence Day, Labor Day, Thanksgiving and Christmas. On all other holidays, only street cleaning rules are suspended, and other regulations remain in effect.