Tartu is easily explored on foot but there is also a local bus service. You can buy a single-use ticket from any kiosk (€0.83) or from the bus driver (€1.50); be sure to validate the ticket once on board or risk a fine. Kiosks also sell day passes (€2.50).
Parking in the city is metered from 8am to 6pm Monday to Friday and through the weekends in July; buy a day ticket from www.parkimine.ee (€7.50) or pay by the hour at a machine (€0.50 to €1.50). There’s a free lot by Atlantis nightclub at Narva mnt 2.