About 2 miles north of Glen Island on the east side, you'll find Black Mountain Point which is also a great picnic spot; it's a little further north than Sarah and Hazel.
From the lake, you could also hike to the top of Black Mountain which offers stunning views of Lake Champlain, the Green Mountains of VT, the Hudson Valley, Lake George and the Adirondacks. The climb is 2.8 miles and is quite steep from the lake. Visit Adirondack.net for more detailed Black Mountain hiking information.
