Fat Margaret (Paks Margareeta) is the fat end of Pikk street. Built 1511–1530 as an artillery tower to cover the harbour approach, it is 25 m in diameter and 20 m high with walls up to 5 m thick, and it is bolted onto the Great Coastal Gate (Suur Rannavärav), the 16th-century arch that was the town’s front door from the sea. You walk in through the gate. Anyone arriving in Reval by ship came through this hole in the wall, and the museum inside uses that fact as its organising idea. The tower was later a prison — in 1917 a mob broke in and killed the guards — and was rebuilt for museum use between 1978 and 1981.
The reason to buy a ticket is the cog. In 2015 the almost completely preserved hull of a medieval cargo cog — one mast, high sides, the workhorse of North Sea and Baltic trade — was found underground in Tallinn. It is nearly 20 m long, roughly 700 years old, and came out of the ground with almost 700 objects around it. Very little like it survives anywhere in Europe. It is now the centrepiece of the permanent exhibition, and standing next to a Hanseatic hull at that scale does something no altarpiece can: it makes the trade that built every other building on this list physical.
The rest of the museum runs forward from medieval sea trade through sail and steam to modern shipping, with 17 ship models commissioned for the exhibition and around 50 digital and hands-on stations — genuinely good for children, and the reason a family can spend two hours here. There is a rooftop terrace and café over the harbour.
Open Tuesday to Sunday 10:00–18:00 from October to April, and daily 10:00–19:00 from May to September. Ticket sales stop thirty minutes before closing. It is at the north end of the Old Town, five minutes from St Olaf’s and on the way to the ferry terminals.