A true Estonian
Why locals love it?
The place opens very early and offers freshly made sandwiches and pastry (warm from the oven) every morning. The menu that changes daily and is written on the wall is in Estonian, and the staff might not speak perfect english (they will try), but you can just go crazy and pick at random as everything is really cheap as well.
Why you should visit it
If you're looking for true Estonian food experience, then forget about the expensive medieval restaurants and the advertisements in your guidebooks. Find this place and you will get to know what the locals really eat (we happen to find it delicious). Kadri's Cafe offers the typical dishes that taste just like our grandmas cook for us.
Try the boiled pig's tongue ("keedetud (sea)keel"), the truly estonian pie-type-of-a-thing called "karask" or the drink-type-of-a-thing called "kama".