I'm saving the best mountain climb for last - Blue Mountain. This is a great climb in the center of the Adirondack Mountains.
There are two different hikes worth your time near the lake. The first one is up Castle Rock on the northern end of the lake. This mile walk takes you to the top of a rock overlooking the lake. It's easy and family friendly.
The second climb is up Blue Mountain. This climb is challenging, but can be completed with enough time and effort. A ranger cabin and radio tower are located on the summit. Rangers are often available to answer questions about the area on weekends in the summer.
Castle Rock - Easy (less than 1 hour climb to summit)
Blue Mountain - Challenging (1-2 hour climb to summit)
Follow 28 north 30 minutes past Old Forge. Drive through Blue Mountain Lake Village. Follow Route 30 north. The trail begins shortly past the Adirondack Museum on the right.