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.
You can buy a single-journey ticket for € 1.60. You buy it at the front, from the driver. Coins will be appreciated, large banknotes will not be.
If you are going to take several rides during the day, it will save money and time to buy a plastic smartcard in advance from a post office, kiosk and certain stores. Arriving by cruise ship, you have a nearby R-kioski in Terminal A, which is open from 7 in the morning to 6 in the evening (5 p.m. on Sundays).
You pay 2 euros for your smartcard and top it up with a payment for a single-day's travel, 4 euros, so the total outlay will be €6.00. Now all you need to do when entering a bus, tram or trolleybus is touch the card against the orange reader, located by every door.
Actually the two-euro card charge is a deposit, which you can get refunded by returning the card to Tallinn City Council at Vabaduse väljak 7, but who's going to bother with that?
If you've been to Tallinn before, you may remember that people of 65 and over used to travel free on public transport, but that exemption has been abolished.
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.