You won't have too much trouble as long as you keep to the center of the city. As in pretty much any Eastern European country, anybody under the age of 30 can speak english more or less acceptably. And expect to get ripped off by taxies if you don't speak at least one local language.

I'm slowly trying to learn Estonian from the Byki software package, but as a general rule, anyone young can speak english just fine, and even old people (My landlord is 60+) have a passable grasp of the language.

Dealing with the phone company has been simple, they have a menu option from the Estonian main menu to choose English, and although not all their staff speaks English, they can understand you when you ask to speak to someone who can.