Flying directly to Tartu:
You can travel from Tallinn to Tartu by bus or by train. The buses leave from the central bus station every 30 minutes in the daytime, but there are only a few buses during the night. The full-hour express buses between 7 am and 8 pm also stop at the Tallinn airport (at stop no 2). So you can catch the bus to Tartu from the airport. We reccommend you to buy the ticket in advance from the internet http://www.tpilet.ee/en? or use the self-service kiosk in the airport passenger terminal. Starting from the airport, choose the station Tallinna lennujaam as a starting point. Note that bus tickets bought via internet should be printed out. You can buy tickets, check the timetable and prices at http://www.tpilet.ee/en? You can also buy the ticket directly from the bus driver but it is better to ensure yourself a seat in advance. The official travel time is 2 hours 25 minutes.
If you arrive at the Port of Tallinn and you do not have a lot of luggage and the weather is nice, you might like to walk to the bus station. You can check the route from Google maps, it is about 3 km. (The distance from the airport to the bus station is actually the same but the route is not half as pleasant.) If you do not wish to walk you can catch bus No. 2 which runs between the port and the airport and stops near the bus station (the stop is called “Autobussijaam”). Also a bus line 90K (Hansabuss) is traveling between the port, city center and airport, you can check the route, stops and timetable here: http://www.hansabuss.ee/index.php?page=246&
If you take a taxi, please check the price before sitting in. All taxis must have an official price list displayed. A 3-4 km ride should cost about 10 €. We recommend Tulika Takso (http://www.tulika.ee/Index.aspx?&Link=1) and Tallink Takso (http://www.tallinktakso.ee/en/content/default.htm).
It is also possible to travel from Tallinn to Tartu by train. Usually there are only two trains during the day: one in the morning and one in the evening. You can check the schedule here. The trains leave from the Balti jaam which is within walking distance from the Tallinn port.
You might also want to consider flying to Riga (Latvia) which is about 250 km from Tartu. The bus ride takes 4-5 hours (Lux Express or Ecolines). You can also travel by train changing in Valga which takes about 5 hours.
Getting around Tartu:
Tartu is a nice small town where everything is within walking distance, including the bus station and the railway station. If you have a lot of luggage or you just don’t feel like walking, you can get a taxi which should cost less than 10 € for most distances. More information can be found on the Tartu tourist information website.