First off i just want to say i loved Lake Placid and Whiteface. The first day i got there me and my friend went snowboarding while my sister and here boyfriend went site seeing. They said that the ski jumping place was amazing, they went to the top of the towers and everything. If your luckey you could see them practicing. They then went to the bobsledding, which they said was also very cool and very fun. The torch is by the ski jumping, and from what my sister said, and from what i seen, it was not up to par of what i thought it would be. It looked like it was not even taken care of. The final thing they saw was the river and waterfalls, which was frozen over, but you could walk onto a bridge and come very close to the waterfalls.
Now for the mtn, Whiteface. It was an amazing mountain, by far the best mtn ive ever snowboarded on. It seemed like a lot of locals which was also nice. The gondola was very nice, becuase you could get nice and warm on it. Whiteface can get very, very cold, so i would recommend dressing heavy. Also you said that you had a 9 year old skiing with you, just to warn you they have some very hard trails there, so keep an eye on the type of trails (diamond,green, blue). Also dont be afraid to take her up to the top becuase they have a blue that is very easy that goes down.
Like I said, it was an amazing trip, and the best 3 days of my life.