Dinos to diamonds, bears to beetles, hissing roaches to African elephants – this museum will take you around the world and back, across millions of years in time. It’s all housed in a beautiful 1913 Spanish Renaissance-style building that stood in for Columbia University in the first Toby McGuire Spider-Man movie – yup, this was where Peter Parker was bitten by the radioactive arachnid.

The special exhibits usually draw the biggest crowds, but don’t miss out on a spin around the permanent halls to see such trophy displays as the Dinosaur Hall, featuring the world-first T. rex Growth series. Historical exhibits include prized Navajo textiles, baskets and jewelry in the Hall of Native American Cultures. If diamonds are your best friend, head to the Gem & Mineral Hall with its walk-through gem tunnel and a Fort Knox–worthy gold collection.

Kids will have plenty of "ooh" and "aah" moments in the spruced-up Discovery Center, where they can make friends with Cecil the iguana and Peace, a 9ft boa; dig for dinosaur fossils; handle bones, antlers and minerals; and get close to tarantulas, scorpions and other creepy-crawlies.

For grown-ups, the museum turns up the volume during its First Fridays event series, which combines brainy lectures, live music and KCRW DJs in the African Mammal Hall, two bars and late-night access to the exhibits, which are all bathed in nocturnal light. Check the website for upcoming dates.