Suggestions:

Get up a Mountain

Get on top of one. If you can't climb you can drive and take an elevator to the top of Whiteface. The highway and Castle on the top were built in the 30's and are both attractive. You can also get close to the summit on the gondolas at Whiteface Mountain Ski Center. There are mountains of every size and you won't regret the hike when you stand on the summit. You can ask people which peak is right for you. (Cobblehill is practically in town and though tiny packs a nice view.) Other favorites include Cascade, and Mt Joe

Jump in the Water

The water in the taps in LP comes out of the lake. State law mandates that's its treated, but a few years ago it just got pumped from lake to faucet. The water is clean, cool. You can swim in the rivers and lakes. Do it. You'll feel wild again. You can drive out to the base of the High Peaks on the Adirondack Loj road and swim in Heart Lake, or follow one of the trails to waterfalls and swim in a rock pool in water that will define "refresh".

The Palace

On Main Street, a treasure of a Movie Theater, and the place to gather with your group. They guy who owns it usually takes tickets, and he's kept it old and beautiful. There is even an original organ that sometimes gets turned on for silent movies.

Taste the Food

There are a surprising number of good food places. Cafe Rustica, Interlaken Inn, The Lake Placid Lodge, top the list of higher end food. Burgers at Lisa Gs, which is a local family hang out. Chair Six is tiny, but the best breakfast in town. 

See the Wild Life

If you want to get into the nature of the Adirondacks you should go to The Wild Center. It's the best place to get what makes this six million acre Adirondacks so cool. Live animals, movies, hands-on lots of smart exhibits, and really nice guides.

Go to an event

There is always something on in town. Horse Show, Olympic style hockey, Iron Man, world class winter sports events (bobsleds, luge, ski jumps). The whole place feels like, well, an Olympic village, and it's fun to feel the energy up close.

Explore the area

Lake Placid is the capital village of the Adirondacks, and most people who live here head out into the neighborhood. Recommended - Essex on Lake Champlain - historic port town on the big lake.  A great drive, and Essex is a nice spot to walk. Fort Ti is the best American Revolution thing you can do. High Falls Gorge puts you deep into the canyons of the Ausable river and its waterfalls.