Many of the artists whose work is on display at this small West Side museum come from outside the art world. Intuit exhibits the work of self-taught and outsider artists like Henry Darger, an outsider artist whose cramped Chicago studio has been recreated inside the gallery. Darger's trademark blend of nostalgia, horror, and camp consumed reams of paper and nearly every corner of his apartment.

A lone vault in green, grassy Lincoln Park, Couch Tomb is the most visible reminder of the park’s previous life as a public cemetery. This stone mausoleum was built in 1858 for the hotelier Ira Couch. It is often described as the oldest structure still standing in the path of the fire that tore through the city in 1871. Mysteries abound about how and why the structure stayed put, and just how many bodies are interred within.

This stately museum is housed in a chateau inspired by Le Petit Trianon at Versailles. Inside, you'll find a mix of hard science and compelling curios. Don’t miss the diorama of an operating theater, where a patient’s body would be on display to hundreds of onlookers, or the jumble of stones that once clustered in kidneys and other organs and now look more than a little like pieces of coral.

Some of Chicago’s most prominent architects and cultural figures were laid to rest in this rambling cemetery. It's filled with dramatic (and odd) graves like the Ryerson Tomb, which was designed by Louis H. Sullivan and inspired by an Egyptian pyramid. Pay a visit to William Hulbert, too. He was part-owner of the Chicago White Stockings, which predated the Cubs, and his gravestone is fittingly shaped like a baseball.

Every inch of this shop is full of wonders, some more morbid than others. Offerings range from shells and insects to bloated things in jars, stuffed jackalopes, dental X-rays, bodybuilding pamphlets, and a papier-mâché King Kong. You could easily spend hours taking in the shelves and display cases, but be sure to look up—you don't miss everything dangling from the ceiling.

To witness what is arguably the most magnificent Tiffany glass dome ever made, head to the Chicago Cultural Center and look up. The 200-foot-diameter dome in Preston Bradley Hall is touted as the largest in the world—with 1,134 square feet of colorful mosaics and 30,000 individual panes of glass, the boast seems valid. The dome's smaller, but no less alluring counterpart can be seen in Grand Army of the Republic Hall.

A melange of bitters, tea tree oil, and chamomile float through the air at this small apothecary on the north side of Chicago, which has been serving Chicago since 1875, when pharmacist Peter Merz first opened the shop. Though it moved to a new building in the 1980s, the pharmacy's hand-carved wooden facade, tin ceilings, and oak cabinets pay homage to the original design.

This natural history collection already appears on many tourist itineraries, but you might be surprised what you can find inside its nooks and crannies. Dodge crowds in the great hall and march straight to the N. W. Harris Learning Collection, a lending library of 400 miniature dioramas full of taxidermied fauna and plastic flora. Exhibits range from a mounted barn owl with outstretched wings to a miniature model of a gold mine and a step-by-step tableau about processing wheat into flour.

When artist Theaster Gates snapped up this former bank for just $1 in 2012, the once-elegant building had fallen ramshackle. These days, it’s all freshened up and serves as an epicenter for art and activism. It houses rotating exhibitions and permanent collections including an archive of 60,000 glass lantern slides from the nearby University of Chicago and the vinyl collection of Frankie Knuckles, the “godfather” of house music.

Willie Dixon’s Blues Heaven Foundation houses records, performance gear, and more. It's all inside the former stomping grounds of Chess Records, the label that once claimed such venerable acts as Etta James, Muddy Waters, Chuck Berry, and Bo Diddley. Drop in for a tour or to groove to concerts in the garden.