We did this last year (with our 3 kids!). Kind of a bust. Not particularly impressive fireworks and it was crazy busy with people. We ended up on Fulton Street I think. We were a few blocks back from the river, and our view was partially obscured by buildings lining the street (might be why we didn't think it was that impressive).
We showed up maybe 30 minutes early, so didn't get a great spot. I just remember the stink. Sewage and marijuana. The guys around us kept marveling at how awesome the fireworks were, so we wonder if maybe we did get the real NYC fireworks experience.
As for exiting the fireworks, if you're taking the subway, I'd suggest hanging out at a city park or somewhere else for 30-45 minutes after the fireworks end. There were crushing crowds trying to jam all the financial district trains when we went so we tapped out, went to the City Hall park (or whatever it's called), ate snickers and doritos, watched a meth addled crazy get carted off in a wheelchair with restraints, and then caught the subway home after about 45 minutes (from a different line that didn't run along the east side of Manhattan where most of the crowds were). It wasn't crowded at all.
We were lucky to end up in Montreal a couple days later where the international fireworks competition is held. Truly amazing fireworks and not nearly as crowded (we walked down to the waterfront from our dirt cheap airbnb rental apartment). I think they have fireworks almost every Saturday in the summer and some Wednesdays.