Public transport is free in Tallinn. We, locals, pay for it with taxes. Technically, transport is free only for locals, but there are no controllers. Haven't seen one in 4 years, nor my friends. So take busses, trams and trolleybus (August 2017)
It should be easy to blackride public transportation system of Tallinn. It is possible to buy a chip card (Tallinn Card) and use transport for free (in exchange for all the travel data going to some database). You can enter vehicles (buses, trolleybuses, trams) through any doors and without checking. Controls are rare (locals I talked to met them 1-2 times in several months). Supposedly when they happen, it's hard to escape. If you wish to buy a ticket, you may do so at the driver or buy some e-ticket. Prices are around 1.10 EUR for 1 hour, 3 EUR for day, 5 EUR 3 days etc. When you buy ticket at driver, it is more expensive. (July 2015)
Hitchhiking a boat to Finland, especially in summer and on the weekend (when many Finnish come for a 2 days trip) is a very doable option. Whether motor or sailing boat, just go to the marina located eastwards of town and be patient, it should be really easy. Read more from Hitchwiki.
As alternative you may try:
Ferries to Helsinki or to Sweden
If you're traveling with Finnish friend and they have S-Etukortti (local bonuscard), you can get 4 euro discounts from Viking Line. You must show bonuscard when entering the ferry.
Hitchhiking to Saint Petersburg might be quite easy, granted that you have a valid Russian visa or entry.
Street hosting works pretty well, though is better searching for it not in the very historical centre since it tend to be quite touristic (you might find friendly and helpful workers though).
Internet hospex community should also be big enough to easily find a host. In July 2013 Fede and his brother got some 20+ negative answers through Couchsurfing which pushed them to successfully go for the street option.
Tallinn airport is a good option for emergency overnight stay. Bus no. 2 goes there (until 11 in workdays from ferry terminal). Security doesn't bother you. Electric plugs, nice wifi, bathrooms.
Cafes, bars, restaurants
- Old town is very touristic and pricey. Locals don't go there so much.
- Kalamaja district has a boom of local food restaurants (take a tram 1 towards Koplin, 10 minutes from the center. Telliskivi stop would do.)
- Kukeke. Home food place popular among art and culture people. Address: Telliskivi 57, Kalamaja / Pelgulinn district.
City centre is very touristic and busker friendly.
You might have quite a lot of concurrence (especially during the high season) but you'll manage for sure to find your spot and slot of time.
Euro currency, tons of tourist, usually friendly police approach -> usually very good salaries.
Tallinn is great for busking. A lot of finns come for cheaper drink and cheaper prices to Tallinn. 2017 in summer had record of finns visiting Tallinn.
Some buskers come from different coutries. Try to play at Viru street. This is money spot. Tammsaare park is decent too. But Viru street is best.