Does ZipCar accept newly licensed drivers? You would need to check into that because you must be accepted by their insurance company, since it's a car sharing service, not rental agency.
Insofar as dealerships where you may have some luck in the NY-NJ-CT Tri-State Area, I have had luck with more than one of the Ray Catena dealerships, and also The Premier Collection. The closest Premier to you would be in West Nyack, NY, but it could be worth a trip to Rockland County. They have a Mazda dealership, though I am most familiar with two of their Volvo dealerships, but might have a decent used car on one of their lots. You can search their pre-owned offerings from the main dealership pages; however, the Catena dealerships, in particular, might tend to filter used cars by brand and type, relegating anything that doesn't meet their criteria to an auction.
NY BMW, NJ Lexus, NJ Porsche, NJ Infiniti, NJ Jaguar, NJ Mercedes-Benz and other locations offer certified preowned luxury cars from the
The Premier Collection
Some models you may want to consider would include a Mazda 3, and even a Volkswagen Golf, provided it's from the last couple of years when the quality was significantly improved. A pre-owned Civic or Accord would also be a good bet, though with any vehicle that's used, you need to get an independent inspection from a company like Carchex.
You mentioned Chrysler earlier, but they can be very finicky to own, and I am suspicious of them on the used car market, unless it was a fleet purchase/lease/rental car. Used Volkswagens can also be similarly suspect, especially Passats and Jettas, but the Golf is a bit more upscale, but maintenance is in line with a BMW, don't forget, as it's not as easy to work on as some other models.