National Museum of Scotland

Dolly the Sheep stands in a glass case on the first floor, looking remarkably calm for an animal who changed the course of biological science. Born at the Roslin Institute just outside Edinburgh in 1996, Dolly was the first mammal cloned from an adult cell, a breakthrough that made Edinburgh the unlikely capital of genetic revolution. She lived six years, developed arthritis and a lung disease, and was euthanised in 2003. Her taxidermied body ended up here, next to a display explaining why cloning a sheep was the easy part — the ethical questions are still unresolved.

The museum itself is two buildings stitched together: the Victorian-era Royal Museum, with its soaring Grand Gallery of cast-iron columns and glass roof inspired by Crystal Palace, and the modern Museum of Scotland, a sandstone drum designed by Benson & Forsyth that opened in 1998. Together they house over 20,000 objects spanning the entire sweep of Scottish and world history, from Pictish stones to particle physics. Admission is free, which makes it the best free rainy-day option in a city that has quite a lot of rainy days.

Among the treasures are eleven of the Lewis Chessmen — twelfth-century walrus ivory pieces discovered on the Isle of Lewis in 1831, their bulging eyes and bitten shields making them the most expressive chess set ever carved. The Monymusk Reliquary, a tiny eighth-century casket said to have been carried before the Scottish army at the Battle of Bannockburn, sits nearby. There's also a full-size Tyrannosaurus rex skeleton, a working Watt steam engine, and the Maiden — Edinburgh's own guillotine, which beheaded around 150 people between 1564 and 1710.

The rooftop terrace on the seventh floor offers one of the city's best free viewpoints, taking in the castle, Arthur's Seat, and the Pentland Hills.