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.
An attempt at an answer as a guest, because I do not have an account, so cannot comment, and may have spotted a couple details in passing.
Feel free to delete this answer and just add to Mark's
Mark as provided the evidence for a Pennsylvania or Tennessee class cruiser. On Wikipedia, the picture for the Pennsylvania shows 4 casemate guns on the upper deck, and the picture for the Tennessee 5 casemate guns.
The ship in the question as 4 casemate guns on her upper deck, not 5. Also, the difference in hue between the hull and the upper works would match the colors on the Pennsylvania picture.
Therefore, I would wager she is a Pennsylvania class, not a Tennessee.