I don't know your budget, but we hired Frank Ahn Films. He has the best reviews, and all of the highlights he has on his website made me cry. And those aren't my own wedding. He's based out of NYC but is doing our Bronx/Westchester wedding.
ETA - do you have a photographer already? If so, do they have someone to refer you to? Generally, hiring someone that your photographer has already worked with is preferable, since they will have to work closely the day of. That's how I found out about Frank Ahn Films.
With a video budget of $2k some of the ones I mentioned have packages in that range including NST Pictures. You won't get all day coverage and you'll get only one videographer, but you'll be able to capture some special moments and that should be just enough!
When we were looking we also looked into Silver Fox Photography which had great packages.
There were a few other studios we looked into but were between Studio 27 and SilverFox.
I was actually going to go with Silver Fox because they were cheaper than Studio 27 but when I called Studio 27 to let them know we weren't booking with them they actually price matched SilverFox and then wen lower! So I would also recommend negotiating where you can! Its definitely possible!
They were really nice to communicate with, and they were high on our list-- the only reason we picked someone else was b/c our videographer's style was a better match to our photographer's, and they had worked together a ton before.