You can get information while in Tallinn from the tourist info as well to collect information on-line in advance. Tallinn city has a nice official web site, there is general information about the city and also including lots information for visitors.
The site is available also in English & Russian
Direct link to the tourism site
Estonia is probably the most modern country concerning the Internet: In local government council elections hold on 16 October 2005, voters in Estonia were the first in the world who had the choice of voting either from their homes over the internet or in a traditional booth.
People all over the country can access the internet from over 700 Public Internet Access Points (PIAP). The PIAP has a special traffic sign, with the @ symbol, showing its location. Most of PIAPs are located in libraries and other municipal buildings across the country. One can easily locate the nearest PIAP by accessing this website.
As a rule, no fee is charged for using the Internet services at PIAPs. PIAPs should guarantee everyone’s free access to electronic information, and to training where necessary
There are more than 600 areas (city squares, hotels, pubs, airports etc.) that currently provide high-speed wireless Internet access. More information: www.wifi.ee.
A good and central place for a quick mail check is the little coffee bar in this (rather posh) shopping centre. Prices seem to vary winter and summer; the most I paid was about 60 krooni/hour around midsummer.
At the corner of Viru and Vene, computers are under the stairs.
Favorite thing: you can find free and very fast internet access in very many caffees and bars in Estonia. all you need is wlan card for you laptop. more info www.wifi.ee.