If youre trying to go skiing, Stowe, Sugarbush, Mad River and Bolton are all within an hour drive from burlington. For ski shops, the only one in town is the Ski Rack. Nothing to special about it but its a pretty nice shop. There are a lot more out towards stowe and sugarbush though.
As for "cool things" to do in town, Church st is always a good place to start. Lots of shops and good resturants down there