According to Delfi and some other media (Link 1, Link 2, Link 3), Google cars have been spotted on a parking lot near Peterburi tee.
If everything goes fine, Tallinn should get Street View somewhere between 2011 and 2012. I have to say I am a bit surprised that they are starting to take panoramas now and not in the summer. I really hope that they could use Street View bikes in the Old Town.
P.S. Riga already has a non-Google Street View - www.1188.lv