UA serves NYC?
If you're based in DEN, then LGA is probably your best bet from the flight perspective. There are more connecting flights from LGA than JFK including six directs to DEN. IIRC, all flights to JFK from DEN transit IAD.
Some flyers prefer JFK for it's access to SkyTrain, the service where the airport transit connects to public transit (either subway or LIRR). While it's certainly convenient, I find it easier to take a cab into the city, especially if the size of your party is 2-3.
If you're looking for ambiance, JFK has LGA beat on all counts (except for maybe the RCC). LGA is a leaky, dirty, crowded second rate airport, IMHO. At least JFK's Terminal 7 is passable as a portal to the "Capital of the World".
One advantage LGA has over JFK is that the RCC is before security and can be easily accessed as a meeting point.
[Asbestos suit]EWR doesn't exist in my world unless you're a CO fan. Others may care to provide insight on EWR.[/Asbestos suit]
You can find additional NY info
here.