No offense intended rule303, but you are treating this with a common sense approach. This is the Empire State. One might think setbacks and distances between structures would be the main concern. Sorry. We are the Eastern Europe of the US. Common sense rarely applies.
If you've decided to stay in NY, you've decided to give up on your freedoms. And that's fine. Many of us have to make temporary decisions based on personal situations. I'm not questioning yours. I'm a NYer too. As far as shooting on your own land, first off, remember this. In NY, it's not really your land. It belongs to you and all regulating bodies that think they have jurisdiction over you. You also rent it from the local taxing authorities. That depends on where you live. If it's in the Adirondack area, that's a can of worms all its own. That area is governed by the Adirondack Park Agency, a group of wannabes from NYCity who love to tent and raft and paddle and carve things out of wood. But always leave the locals with the responsibility for the taxes. If you're in an incorporated village or town, you have to look into their regulations/restrictions. There's the DEC (Dept of Environmental Conservation), zoning laws, setbacks to consider. If you need a variance from a zoning restriction on use of "your" property, you will need to file a SEQR, or an environmental quality review plan. You will enjoy the necessary public hearings and the expenses involved. Before that, you will have to determine what the lead agency will be for that plan. Most of the time your local officials will try to avoid that responsibility. That avoids, for them, the litigation that follows almost everyone's endeavors here in the Lawyer State. One of the main concerns of that effort is what you plan to do with the lead that will be entering the ground water from your irresponsible use of the environment. I'm sure a hundred thousand spent on a filtration system will do the trick, especially if you hire the local politician's crew to do the construction. If you do get through all this, be sure to secure the support of all who can hear shots fired on "your" land. If this is not a grandfathered or traditional use of the property, anyone who doesn't like to hear a bang can fight you in court or in front of the local zoning board during the process. If you win all this, and get to shoot on "your" land, be careful, as you may end up getting sued as someone could blame their ADHD or earache on your shooting habits. In short my good man, good luck. Here in NY we are ranked 50th in the nation in individual freedoms. We earn that distinction every day. A neat trick when our property taxes are the highest in that same nation.