Café Anglais, Tallinn
Now this is an absolute must (and always pretty crowded, so I might just as well tell you about it). You can find Café Anglais right at the town square, and you will find not just a café. Excellent food and very nice service on the first floor, and all this laced with a sense of culture and art, served with a nonchalant flair that seems to do well among the expatriates in town.
Try the cakes. Try the sandwiches. Try the coffee. Try the cakes again. Sigh...
Slightly less cheap (but only slightly).