Go up to Toompea Castle
Toompea Hill has always been the core of power in Estonia. Various rulers of Estonia have changed the Toompea Castle to their liking over the last 800 years, starting with the initial stone structure built by the German Knights of the Sword in the 13th century and eventually turning into a tickle-me-pink Baroque palace, courtesy of Catherine the Great. It's now home to the Riigikogu (Estonian parliament), which commemorates the country's independence by raising the national flag atop the 14th-century Tall Hermann tower every morning.
Tourists can take free guided tours of the Toompea Castle in English, Russian, or Estonian on weekdays, with advance reservations. You'll get to explore the inside of the rosy building, hear about its storied past, and learn about the structure of the Riigikolu. After your tour, walk 500 meters northeast to the Patkuli viewing platform for an epic panoramic vista of Tallinn. From here, you can see straight down to the port.