I found this photo in a relatives old photo collection. Most of the photos were taken around 1905 so I assume the ship photo was taken around that time. A lot of the photos were taken in upstate NY around the Hudson River Valley.
- An American flag.
- Four stacks. Most early US Navy cruisers had one to three stacks.
- A twin-gun turret. This distinguishes it from the St. Louis-class cruisers, which had only only casemate guns, and from the Columbia-class cruisers, which had single-gun turrets.
- Solid masts. In the 1911-1912 timeframe, the Pennsylvania and Tennessee cruisers were refitted with lattice masts to reduce weight.
If the photograph is from 1905, then the ship is one of USS Pennsylvania, USS West Virginia, USS Colorado, or USS Maryland, as the other ships of those two classes were commissioned in the 1906-1908 timeframe. There's a decent chance that it's the USS West Virginia, since that ship served with the New York Naval Militia.