My own 5 favourite experiences:
Flo Kasearu House Museum - Tallinn
Väljasõit rohelisse - Tartu 1860-2014, various artists, Kunstihoone, Tallinn
Merike Estna: Blue Lagoon & I am a Painting - Kumu, Tallinn
Man&Woman - anticipation - Pärnu New Art Museum
Streetart in Tartu
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Overview of all my visited exhibitions and my other art experiences in Estonia during summer 2014:
http://virtualwallworld.blogspot.no/2014/09/feeling-queezy.html
http://virtualwallworld.blogspot.no/2014/09/marge-monko-you.html
http://virtualwallworld.blogspot.no/2014/09/ene-luik-river-of-tears.html
http://virtualwallworld.blogspot.no/2014/09/mare-mikoff-post-time-sculptures.html
http://virtualwallworld.blogspot.no/2014/09/valjasoit-rohelisse-tartu-1860-2014.html
http://virtualwallworld.blogspot.no/2014/09/teemu-maki-how-to-be-man-or-woman.html
http://virtualwallworld.blogspot.no/2014/09/urmas-orgusaar-flashback.html
http://virtualwallworld.blogspot.no/2014/09/the-homunculus-collection.html
http://virtualwallworld.blogspot.no/2014/09/flo-kasearu-house-museum.html
http://virtualwallworld.blogspot.no/2014/09/archeological-festival.html
http://virtualwallworld.blogspot.no/2014/09/ornamentaalne.html
http://virtualwallworld.blogspot.no/2014/09/sirja-liisa-eelma-waiting-room.html
http://virtualwallworld.blogspot.no/2014/09/ulvi-haagensen-cleaner.html
http://virtualwallworld.blogspot.no/2014/09/man-woman-anticipation.html
http://virtualwallworld.blogspot.no/2014/09/anonymous-boh-10-new-commandments.html
http://virtualwallworld.blogspot.no/2014/09/august-kunnapu-green-mirror.html
http://virtualwallworld.blogspot.no/2014/09/merike-estna-blue-lagoon-and-im-painting.html
http://virtualwallworld.blogspot.no/2014/09/polymer.html
http://virtualwallworld.blogspot.no/2014/09/public-art-at-kumu.html
http://virtualwallworld.blogspot.no/2014/09/raul-meel-dialogues-with-infinity.html
http://virtualwallworld.blogspot.no/2014/09/black-house-notes-on-architecture.html
http://virtualwallworld.blogspot.no/2014/09/streetart-in-tartu.html
http://virtualwallworld.blogspot.no/2014/09/streetart-in-tallinn.html
http://virtualwallworld.blogspot.no/2014/09/lillekula-stop.html
http://virtualwallworld.blogspot.no/2014/07/sonum-seinal-parnu-estonia-august-2013.html
- or just scroll down from here (or go to older posts)