Base yourself in Tallinn and spend your first day exploring all the nooks and crannies of the Old Town. The following day, do what most tourists don't – step out of Old Town. Explore Kadriorg Park for a first-rate greenery and art fix, then hit the wonderful Estonian Open-Air Museum. On your last day, hire a car or take a day tour to Lahemaa National Park.
Spend your first three days in Tallinn, then allow a full day to explore Lahemaa before bedding down within the national park. The following day, continue on to Tartu for a night or two, and then finish up in Pärnu.