The town itself is not very big, you can explore it by walking. In skiing season there are ski buses around the Ylläs mountain, single ticket is around 2 euros.
In the Ylläs mountain there is a skiing area, most people come here for skiing. There are downhill slopes and also 330 km of cross-country skiing tracks. The downhill tracks are not so long if you are used to slopes in the Alps, but they are very well maintained. The cross-country tracks provide a wonderful journey in the nice forest of the Finnish Lappland, and they are also well maintained. 38 km of the cross-country tracks are floodlit at night.
Rest of the year
The area is very good for hiking, there are a lot of wilderness houses where you can spend a night if your trip does not end even until late night when the sun starts to go down...
In the lower part of the town there is a K-CityMarket where you can buy everything you need. Prices are a bit higher that in K-CityMarkets in south Finland.
There are restaurants, but most of them are open seasonally. In skiing season all of them are open.
Near the slopes there are hotels, you can search and you will find them. If you are on a budget (and/or you want something traditional) you can rent a wooden cottage instead. If you really want to feel the wilderness you can rent a wooden cottage from the National Park (office is in the town), it's cheaper but no electricity or water, heating is with fire, nature toilet.