Go to the tourist office in town for details about renting a paddleboat, or about scuba diving. You can also get an English language hiking guidebook that will lead you to some trails up into the mountains above the lake. You can even hike to the famous ice caves that are nearby if you are in good enough shape.
The Hallstatt area is a great place for some great hiking. Especially if you go up to visit the ice caves. Definitely worth the trip. Not only do you get to see the amazing ice formations, but you also have a spectacular view of the Hallstattersee from up there. You don't have to climb the full 2000 meters. There is a Gondola.
Equipment: Just your run of the mill hiking equipment, but bring a jacket as the temperatures drop quite quickly at altitude.
Fresh Powder almost everywhere! Great conditiions, great slopes, take along a camera and you will have breathtaking views of the Austrian Alps that you will regret not taking a picture of. The mountain has some of the best conditions for skiing I have ever had the pleasure of skiing. Highly recommended. Kasberg is my favorite but there are soooo many good places in Austria
Every once in a while you will find a small Stuberl or a small Huette with great traditional dishes. Some ski places also offer views of must see sites like the Dachstein area with a spectacular view of Hallstatt (the oldest Celtic community in Austria).
Equipment: You can bring your own equipment but rentals are available.