The New York monument near the Craven's house is actually for Ireland's Brigade. This brigade, composed of the 60th, 78th, 102nd, 137th and 149th New York, was formerly Greene's Brigade of Culp's Hill fame. Four months later they are the ones attacking a rock strewn hill. The modern pictures don't really show how narrow of a plateau this is, the older pictures though do show it, primarily because of the difference in vegetation. The cannon in the top picture is a Confederate position, the Craven's house would be over our right shoulder, I'm sure there are times the shadow of the New York monument falls on the Craven's house.
Looking out into Chattanooga.
The rock outcropping on the left is the palisades at Point Park (which will be coming up in a future post), that hotel is no longer there. The New York monument is in the fuzzy part of the scan on the right side of the picture.