Saint Olav's Church
This 12th-century church, at the end of Pikk Street, is the most beautiful in Tallinn. It's also the most unlucky: it has been hit by lightening at least eight times, and burned down three times. Once the tallest structure in the world, its 124m spire can been seen from all over the city. Climb the narrow stairs to the observation deck at the base of the spire for sweeping views.
Kiek in de Kök
The museum inside this great artillery tower (whose name means "peep into the kitchen" in Low German because from the upper floors soldiers could peer into the houses of the lower town) is interesting, but don't miss a guided tour of its limestone bastion passages, which reopened in March with new video and sound effects. Built to conceal the movement of soldiers, the 500m of passages (half are still being dug out) were used as a bomb shelter during the 1944 Soviet bombings, and inhabited by a large community of homeless people in the 1990s.
Old Town
Katariina Käik (St Catherine's Passage) in the Old Town, lined with craftsmen's workshops, is a favorite for many visitors, but I love Pikk Jalg, or "Long Leg" (there is also a short, steep alley called Lühige Jalg, or Short Leg), which winds up to Toompea Hill. Stop on the way for coffee and a croissant at Bonaparte, a charming French bistro (Pikk 45). At Toompea Hill are the Great Russian Alexander Nevsky Cathedral, St Mary's Cathedral (the oldest church in Estonia, founded in 1219) and several viewing platforms, where you can see over red-tiled roofs to the Baltic Sea.