The closed market (Tartu Turg, Vabaduse pst. 1) is *the* place to buy meat. You can find anything you've ever wanted (as long as it is pork) at a 20 to 50% lower price than in a supermarket - and some other kinds of meat too. There's also a wide selection of average but affordable cheese, plus a fish section... and some candy, too!
Clear highlight, apart from the fresh meat itself, is the Rakvere meat stall. You can find all sorts of meat that has to be eaten in a day or two, but is sold at pretty ridiculous prices. 1 kg of šašlõkk for 2€? Chicken with yogurt sauce for 3€/kg? Sure, why not! What is available depends on what products are nearing their expiration date on that specific day, but it's pretty unusual not to find at least one decent product for a full meal in there.