There are tons of activities at Lake Placid as this is, afterall, a tourist village. The town itself seems fairly small; it feels like it was built specifically to serve the needs of athletes/tourists and be the Olympic village (who knows, maybe it was, I didn't ask). Actually, let me back up a step...
According to Wikipedia, Lake Placid, NY was founded in the early 19th century to help with operations of iron ore mining. A man by the name of Melvil Dewey founded a social & recreation club there (on Mirror Lake) in 1895, which drew rich & famous to the area. The Lake Placid Club was the headquarters for the International Olympic Committee for the 1932 and the 1980
Winter Olympics in Lake Placid. Many of the Olympic facilities are still in operation and offer unforgettable experiences for visitors (of course, some activities are rather $$$). There are also a number of sporting events and other festivals that take place every year.
Some people find it a bit weird that the village is called Lake Placid considering it's mostly on Mirror Lake...
But I digressed... First thing's first!