You do cover all three airports. As of late there have not been any EWR trips in the bid package, but that does not mean that they will not have you go over there to pick up a ATL or CVG rotation.
Most of the flying is out of LGA, but there is some JFK flying. Most of that goes to the senior guys that are out of the island that want to get off early, or late. (Turns to FL)
That said, there are generally day lines ( shuttle, four legs, or FL turns ) two days, and three days during the week. Some four days on the weekends for the shuttle trips, and occasionally you will have a trip that will come through ATL and CVG.
The flying is nice, but is generally built for people that live in the area. If you commute you will need a crash pad. Expect there to be movement out of NYC with this entitlement, so your QOL should increase quickly.