Explore
If you are near Tallinn, the Telliskivi area is hipster and fun to explore. They have pop up shops, art areas, and fun restaurants. Old Tallinn has castles, churches, restaurants galore, medieval fairs, archery, and architecture dating back to the 13th century. One day in Tallinn will give you a great understanding of Estonian history and culture.
Take a ferry to Finland!
If the weather is warm, spend a day in Tartu or Vilijandi. Tartu has a beach area along the river, which is perfect for swimming. In Vilijandi, there is a beach not too far from old castle ruins.