I know most people who visit Estonia see only Tallinn, and very briefly. For those considering more time in the country, I recommend checking out the Estonia Museum Card. It's valid for 12 months, costs 59 euros, and covers entry to over 100 museums. In compiling a list of places I may want to see, I've found few museums and galleries that aren't covered. Other tourist attractions generally are not participating at this time.
It appears that one is allowed to visit participating sights more than once: "The total number of visits during the period of validity of the Museum Card is not limited but only one visit per day can be registered in each place of visit."
I'm looking forward to using the Museum Card when I visit Estonia in July. I really like long-validity passes like this, because I can go about my sightseeing without worrying about cramming specific sights into a short period of pass validity.