Essentially, there are only two things to do in Zakopane - hiking and skiing. If you like neither, then you might not enjoy Zakopane as much. There are three main ski slopes in Zakopane - Nosal, Szymoszkowa and Harenda. If you are new to skiing, you should start out with Nosal for a day. Szymoszkowa is more for intermediate skiers, and most people can reach the intermediate level after a day or so. Harenda is a great place to entertain beginners all the way to advanced skiing. If you have some experience in skiing, try out Szymoszkowa for 2 days, and then go to Harenda for a different experience. Note that sometimes, you do not need a ski pass to ski. For example, if you are a beginner, you can just play around at the bottom of the slope. Ski pass is only needed to take the ski lift. Try watching ski videos before you hit the slopes, and if you really have trouble, you should take 1-2 hour of ski lessons. They will pay off for sure.
My advice is to stay at Target Hostel, as the location is superb. It is a 8 min walk from the bus station that you drop off from if you are coming from Krakow, Warsaw, etc. It is also a 3 pln, 10 min bus ride to all the 3 ski slopes, which gives much flexibility. Finally, it is another 8 min walk to the Main Street of Zakopane, where there are plenty of affordable restaurants.
For hiking, there are numerous routes that you can attempt, but all of them are subjected to the weather, your gear and ability. The one that I went to was called Morskie Oko, a crater lake that is part of the Tatra National Park and is the largest and 4th deepest lake of the Park. The transport to the bottom of the hike is 10 pln for 1 way (40-50min), and then you can take the horse cart up for 20 pln (1 hr 10 min). Or you can just walk your way up (2-3 hr). Remember to wear boots or you may really struggle to ascend. At the lake, there is also a nice restaurant that sells great potato cakes, a must try!
