Taxiing to 22 would require crossing 13/31 at a nasty point. It is better (easier) to land into the wind than it is to takeoff. So therefore if the wind is:
North, land 4, takeoff 31
Northwest, land 31, takeoff 4
West, land 31, takeoff 4 (or 31 using single rwy ops, depending on strength of wind)
Northeast, land 4, takeoff 13 (or 31, depending on the wind)
East, land 3, takeoff 13
Southeast, land 22 (or 4, depending on the wind), takeoff 13 (it is very rare to land on 13)
South, land 22, takeoff 13.
Southwest, land 22, takeoff 31.
Keep in mind, in the NYC area, its not only just that airport that decides what runway to use. All of the NYC runways face the same direction:
JFK: 4/22 L/R, 31/13 L/R
LGA: 4/22, 31/13
EWR: 4/22 L/R, 29/11
TEB: 6/24, 1/19
Some of those must match (ie TEB/EWR, LGA/JFK) due to their close proximities. So if one airport wants to change direction, then they all must. Usually this isn't a problem as the winds are generally similiar. To get a feel for it, look at the departure instructions for LGA 13, HPN 16, JFK 31s, any of EWR, or any of TEB. They all require some fancy maneuvering to stay clear of other airport's traffic areas.