Right beside Lake Placid, Whiteface Mountain was one of the most recommended locations during my last New York trip. Sure enough, the views including that of Lake Placid back-dropped by some of the most significant mountains on the east coast is well worth the journey.
Access can be found more easily via Route 431, though there is a $10/person toll at the base of the mountain, or by hoofing it yourself. Against the recommendations of my friends, we drove and couldn't hike up for time reasons. Just note, the road does close in the winter.
At the top, assuming you drove up, you'll find parking close to the Castle. The Castle houses bathrooms, a gift shop, along with a cafeteria. The hike from here isn't very long, but there is some vertical involved to get your heart pumping a little. I saw individuals of all shapes, sizes, and ages making it up; though it definitely took quite a bit of effort for the less physically capable groups. At best, the trail is paved with concrete and steps; at the worst, you'll find yourself making your way around and over large boulders or rocky terrain. Alternatively, you can also hike up the mountain from the base instead of driving. Since I did not take that route this time, however, I can't provide a lot of details on the difficulty of that way.
When you reach the top, you'll find the Whiteface Observation Tower along with multiple overlooks of the surrounding areas. When you leave, assuming you drove up, be sure to stop by some of the pull-offs along the access road if you didn't on your way in; there are some well worth it views.