Upvote:5
The festival grounds (Lauluväljak) is a bit out of the way but not very far (a little over 3km east of the old city). There are several bus lines going past the festival grounds, including 1A, 8 and 34A from Virus Keskus and line 5 which goes through the old city, each with 2 to 4 buses per hour on Sunday. Some lines go to the Oru stop on the other side of the park.
The buses may be crowded — I don't see any indication of special event shuttles on the even web page.
There are events at the Kalev Central Stadium as well, which is near the long-distance bus station (Autobussijam) at the south-east of town, on tram line 2 and several local bus lines, and slightly under 2km from the old city.