Where do go and what to do in Tartu and Tallinn

Me and my friend are going to Tartu this Sunday, and we are staying 2 days.

• What should we see and do? Any suggestions :)
• Where to drink and eat (in old town/city centre) ?
• Is there some pubs and restaurants for example that are not full with tourists and tourist prices ? (i'm student, so budget is limited).

And then same guestions about Tallinn. We are goming to Tallinn in Tuesday and also staying there 2 days. In Tallin we are staying near the railwaystation.

In Tallinn we are going to see the old town offcourse. But what about eating and drinking, is it tourist priced in old town or in centre, or is there any cheaper and maybe not so tourist focused places to drink and eat.