The driver will pick you up from your address in Riga and on your way to Tallinn firstly will take you to Sigulda - the city, which is located in Gauja National park.
You will have some free time to walk around, later going to visit the Turaida reservoir, where you will have a private tour with the local guide.
Afterwards, you will continue to Tartu, the city in Estonia, mostly famous for its University, which is one of the oldest Universities in Europe. In Tartu, you will have free time to walk around and admire the architecture and the busy life of the students.
Also to have lunch if wanted. Continuing to Tallinn, where you will arrive in the afternoon - the driver will drop you off at your required address.