NYC has one of the best ratios of hospital beds to patients in the entire country. There are a huge number of medical institutions in the five boroughs not only serving a huge variety of patients but also performing a tremendous amount of research. I work at one of those institutions and I can tell you that if they weren't looking to capitalize on/spin off their in-house tech, they are now.
Media and Entertainment. All the major players have HQ's here and where they are so are startups trying to sell them goods and services. Boxee comes to mind (as an innovator and a partner). I dunno where to put Meetup, but I'll put em here.
Commerce. Gilt Group, Etsy, etc.
Fashion. Clothia, Warby Parker.
Finance. The money is here and half the players on Wall Street are looking to get off the Street and start a business with the right technical talent. Not to mention innovation in the trading and hedge fund space.
Government. Mayor Bloomberg is really pushing municipal data as a platform. Check out the NYC DataMine and places like OpenPlans. NYCBigApps is a contest (two years running) for developers to take advantage of municipal data for the betterment of the City and maybe make a few bucks/put a business together in the process. This is only going to grow and I expect some great things to come of it.
There are also tech plays like 10gen, Nodejitsu, various tech incubators like BetaWorks and K2 and cooperative groups like GeneralAssembly and NYHacker.
What I find interesting about the tech scene in NYC is that in addition to R&D there is a huge amount of applied technology due to the confluence of talent and industries. The stuff that is getting made out here has a revenue model out the gate because they are re-imagining and re-inventing pre-existing business with technology as a corner stone. At the end of the day, let's face it, people want to be here in NYC. You know what they say - If you can make it here...