February is usually too chilly to sleep outside properly.

If you have proper equipment (sleeping bag) then you can go to one of the well known tourist parks (even Union Square) and tuck yourself into a corner by the trees. Cops usually don't give a shit about enforcing vagrancy laws, but they do check the popular parks just barely enough to prevent the permanent unhoused people from staking their claim to a spot. 2 nights is low enough risk that you won't have any problems. Avoid the big parks like Riverside or Central. They have their own enforcement and/or the good sleeping spots are definitely claimed.

If you don't have cold weather gear, you can try to find a subway grate that vents the hot air up. Usually these are already claimed. You may be able to sneak two nights in if you go to the richer parts of the city (UES, UWS) where outreach organizations are more active and might have convinced some of the usual campers to spend time in a shelter.

I don't know enough about BK or Queens to give advice for them. BX and SI just seem like bad places to sleep in in general.

But I'd encourage you to first try to be a hobosexual. This city is great for that because we're idiots and we bring a lot of people home for one night stands. There's also a lot of tourists who're looking for an exciting NYC experience. First night in NY I spent in a stranger's hotel room, and that was just as late night drinking buddies.