"Åre Östersund Airport" is located on "Frösön", just outside town. There are four airlines operating at "Åre Östersund Airport".
Stockholm Arlanda - Östersund:
SJ (the national train operator)  has regular service between Östersund and many cities in Sweden. It is a more time-consuming than flying, but if you wish to see the country, a good option indeed. Travel time from Stockholm is 4 hours 50 minutes using the high-speed SJ 3000 train which has a daily service in each direction (in the afternoon from Stockholm, in the morning from Östersund), whereas slower trains take around 8 hours. Keep in mind, however, that Swedish rail traffic has seen severe disruptions in service due to snow the last five years with trains being delayed for several hours and cancelled.
Another nice way to go to Östersund is by the Inlandsbanan. It's a slow diesel train that starts in Mora and ends in Gällivare. They make a stop in Östersund, so you can get on and off the train. The train is rather touristic, but it's a very special way to get to Östersund.
Östersund has a fairly extensive, inexpensive bus system, although you might have a long wait ahead of you if you plan to move about after 19:00, or on the weekends. You can buy single tickets on the bus, or pre-paid cards are a great deal if you plan on a longer stay. These can be purchased at the main bus station in town, located on Kyrkgatan.
Jamtli is an interactive museum about the history of Jämtland. Take the guided tour if you have a chance, the guide is very knowledgeable, and can speak both Swedish and English. The museum suits people of every age; so children can have a great time there.
Take a walk along the lake with its beautiful view.
Take a boat trip around the lake - the 5th largest in Sweden.
It is always interesting to learn about the sea monster "Storsjöodjuret" that is said to be lurking in the lake.
There are two Hostelling International (HI) locations in Östersund: STF Östersund Ledkrysset and STF vandrarhem Östersund Jamtli.
STF Östersund Ledkrysset is located in the center of town and has double and twin rooms as well as dormitory beds. Serves breakfast, dinner and has a small shop. Free internet access. They can be reached by phone at: +46 (0)63 10 33 10.
STF vandrarhem Östersund Jamtli is pretty close to the center of town, and they can be reached by phone at: +46 (0)63 12 20 60.
If you travel with friends and need a place to stay for a couple of nights, you can also find a room at Östersund camping, which is 3 km away from the city center. There is a good bus connection, so it is not a big deal to take a bus and get to any point in Östersund.
Hotel Algen, located near the train station, has nice, large rooms, a sauna, and a good breakfast. Weekend costs are around 694 SEK.
Scandic hotel is one of the most expensive hotels there, but it is centrally located and you will experience its advantages. Starting from 900 SEK per night.