The official Estonian tourism website provides an extensive list of options for accommodation.
camping
You can put up tents free of charge in official "RMK" camping sites. Also there is nothing wrong with camping outside the special site, but remember not to have any fires in places that are not meant for making a fire. Putting up a tent on private land is not allowed- you should ask permission from the owner.
On a warm summer night you may want to experience the feeling of sleeping in the watching tower in Viru Bog. The tower has a roof, so there are no worries about the rain. Sometimes there may be mosquitoes here that carry no disease but are just annoying.Sunsets and sunrises in the bog are unforgetable! (http://www.studioleon.ee/...) (http://www.studioleon.ee/...)
There is no settlement in the bog, bring your own water and food.