While you could get out into Estonia's wilderness on your own, sometimes these kind of adventures are made easier on a tour - where someone else supplies tents, canoes and whatever other equipment you can use to make the trip fun.
If you head out on an adventure outings, there is so much to see, from cliffs, bogs and seascapes to forests, wild flowers and bird migrations. You can trek through wetlands and across tiny islands and really see what Estonia has beyond the cities.
Trek Baltics is one of the companies that does this, and what I love about them is their refreshing approach to making Estonia approachable: for example, they are keen to point out that there are many misconceptions about Estonia, and how they're all wrong!