European-standard mobile phones will work everywhere. Many bars and restaurants also have WiFi hotspots, often without much bandwidth but adequate if there aren't a lot of people online.
Coaches can't navigate the narrow streets of the Old Town and cars are banned from the fine area around the Town Hall Square, so taxis don't help much.
For those unable to walk, bicycle taxis are a good solution.
By decision of Tallinn City Council in September 2012, all Tallinn public transport - buses, trams and trolleybuses - will be free for locals from the start of 2013, but foreigners will need tickets as before. The old exemption for those over 65 has been abolished.
It remains to be seen how (or even if) the ticketing and inspection system will work when it is required for only a tiny fraction of all travellers. Until now, tickets have been available in advance from newsstands, for example in Terminal A, or from drivers.
Consequently, we can't tell you the general price level of taxis in Tallinn. The driver may ask whatever he likes. Cabs that hang around outside late-night bars have been known to charge astronomic fees.
But the tariff must be displayed in the window of the cab, where it can be read by passengers before they step in. If you do not read it first, you have only yourself to blame.
You need not take the first cab in line. Pick whatever taxi, driver or price suits you.