The Institute of Contemporary Art is the cornerstone of Boston’s Seaport neighborhood, now a buzzing shopping district. It was a great place to build a neighborhood around as the ICA features exclusively temporary exhibitions from some of the biggest names in the contemporary art world that will surely challenge your perception of what art can be in the 21st century. The museum’s recently-inaugurated Watershed building, across the Harbor in “Eastie,” is always free.

It’s a good idea to head across the river to Cambridge or Somerville to tap into the Boston arts scene. Check out Central Square and start at Graffiti Alley, where spray painting is legal; what you see one day may well be covered up by someone else’s work the next. Stick around until the evening for live music at the Middle East, a storied complex of several music venues hosting local and international acts. Alternatively, see a local play at the cozy Central Square Theater.

Boston’s North End was once cut off from the city's downtown by highways, but thanks to the Big Dig construction project, that is no longer true. Instead of overpasses, you’ll walk through the Rose Kennedy Greenway to get to the North End’s Italian bakeries and historic sites. The highlight is the Greenway Wall, an old building whose southern face has been taken over by various artists to create large-scale graffiti murals on a revolving basis over the years.

A massive, multi-million dollar renovation brought Harvard University's art museums into vogue again. What used to be three dingy spaces spread across the central campus transformed into a flagship building that is one of the best places to see free art in Boston. Visitors can spend hours wandering through exhibitions as diverse as an Ai Weiwei video installation to a van Gogh self-portrait to ancient Japanese silkscreens.

The MFA, as it’s known, is set on Boston’s “Emerald Necklace,” a stretch of scenic green spaces that ring the modern city designed by Frederick Law Olmsted (who also designed Central Park in New York). The museum houses one of the world's most comprehensive collections of American art and hosts plenty of work from other countries, too. The must-sees include paintings by American artists Winslow Homer and John Singer Sargent, Degas’s sculpture of a young dancer, and Renoir’s Dance at Bougival.

Boston has struggled to shake off its reputation as a stodgy place, but some artists are doing their best to create a welcoming, lively art scene. One of the recent initiatives in that direction is an urban park called Underground at Ink Block, which took one of the least-desirable spaces in the city—an interchange between the I-90 and I-93 interstates—into an 8-acre (3.2-hectare) space filled with commissioned murals, walking paths, and fitness classes.

The Isabella Stewart Gardner Museum is the private collection of its namesake, an art collector and philanthropist who founded the museum around the turn of the 20th century. The building is the highlight—modeled on a Venetian palazzo, complete with lion guardian statues and gushing fountains, around a central green courtyard. This is the place to go for historical art in Boston, minus the 13 works that were stolen in 1990, the costliest art heist in history.

A 30-minute drive from Boston proper, deCordova is well worth a detour. It’s a bastion of outdoor and installation art. Wander at your own pace through the forests and meadows that make up the park, stumbling upon sculptures and immersive installation pieces. In addition to its permanent collection, which counts more than 1,500 individual pieces, the sculpture park features both single-artist and thematic temporary exhibitions.

Forty minutes north of Boston, Salem is well known for being a Halloween hot spot. But away from the Halloween high season, this town still has plenty to offer—including the Peabody Essex Museum, one of the best places to see art near Boston. It’s more than 220 years old, but this museum carves exciting paths for curation: You’ll see exhibits about Black Atlantic culture next to an installation by a Turkish experimental artist next to temporary exhibitions of Rodin.