For grins I went on a search for runway utilization. Found this.

For arrivals, Runways 22 (47%) and 31 (32%) are most common only used. Manhattan would have been on the right side of the plane for most of yesterday's DTW-LGA flights into 22. There's clearly exceptions to flying up the river like today's NKS174 and RPA4339.
From the looks of it,the right side is probably best for runways 22 and 4 (67% of arrivals). The left looks like it's best for runway 31 (32%) (Example) (This flight got a tour out the left)


Departures are evenly split between 31, 13, and 4 at roughly 1/3 each. A 31 departure might get you a manhattan view out the left, but the departure route has a right hand turn just after departure so the city would be behind you and to the left. A 4 departure has a straight out climb before a left hand turn, so you'd get a view from ~30 miles away out the left. A 13 departure has a 180* turn to the left after departure and heads northwest, again with a left-sided view.