Hi Aileen,
The NYC area is indeed saturated... The best prospects right now are the suburbs, places such as Westchester (where my sister just opened her own office) and Northern Jersey. It is still pretty competitive though, so having marketable skills such as implant surgery will help a lot, particularly because there are a lot of affluent communities in these two suburban areas where there is a demand for high-value procedures.
I want to eventually practice on Long Island. It's saturated there too and can be a bit difficult, and probably the simplest way to go about it would be to buy into an established practice where the owner dentist is thinking of retiring. The downside is that such established practices have high valuations and it will take me years and years to accomplish a buyout.
Or I can work towards buying into a group practice as a partner-- I like the comprehensive-services group practice philosophy where a patient can get GP and specialist care all under one roof. There are plenty of these opportunities on LI.
As a last resort, I might take advantage of nepotism..

My uncle who graduated NYUCD '86 has owned his own practice on Riverside Drive and Dyckman (about a mile north of Columbia SDOS, actually) for 15 years, and he is at the stage where he's thinking of taking on a partner for an eventual buy-out as he works towards retirement. The area does offer good possibilities for growth (he gets about 10 new patients a month). The only thing I don't like about it is that I have to commute into Manhattan.
😛
I'm sure there will be plenty of opportunities for you in NYC-- They are out there and might take a bit of looking, but like Frank Sinatra sings, if you can make it there, you can make it anywhere!
HTH!