If you don't mind taking your time to get around, Estonia has good bus and train services. Since the terrain is flat, bicycling is another excellent way to see the countryside, at least in summer. The islands are especially good for cycling. Domestic air travel is expensive. You can get around the larger towns and cities via a variety of trams and buses, although both get frighteningly crowded.
Taxis are plentiful and cheap.
We encourage you to verify any critical information with the relevant authorities before you travel. This includes information on visa requirements, health and safety, customs, and transportation.