Exploring Tallinn's Old Town on foot requires reasonable fitness, with its occasional short steep hills and cobblestones.
Climbing University Hill in Tartu is also somewhat demanding, but otherwise Estonia will rarely present any challenges. Even if you start to tire, you will never be too far from a bus or a taxi.
You will find clear signs both in towns and on trails in the national parks.
Pop into the local tourist information centres wherever you go in Estonia and ask for their leaflets on walking. You will be surprised at the quantity and quality of what you are offered. Usually these are free of charge; if not, the cost will be minimal. Do the same at the information centres in the national parks.
Guided walks in and around Tallinn and Tartu are available – ask at your hotel or local tourist information centre.