Visit the Fogg Museum of Art, located on Quincy Avenue right next to Harvard Yard. It is a first rate art museum with an excellent collection of classical European art and contemporary American and European artists. Some of the highlights of the museum are the series of small works by Rembrandt and Raphael, the collection of French Impressionist, a Canaletto painting of Venice and a first-rate drip painting by Jackson Pollock. There are also two galleries that hang contemporary shows that change on a regular basis (see Resources below).
Visit the Busch-Reisinger Museum, which is located under the same roof as the Fogg Museum, except this unique museum is dedicated to showing mostly modern twentieth century paintings from Germanic speaking countries. It has an excellent permanent collection, a small gallery that houses changing shows and an excellent library and research center on the third floor of the building (see Resources below).
Stop by the Sackler Museum, which is just down the street at Broadway and Quincy. One ticket will get you into both buildings, so one might as well check out the Sackler Museum, while they are in the neighborhood. The Sackler no longer hangs contemporary work, but it still has an excellent collection of antiquities that includes China, Meso-America, ancient Greece and the Middle East.(see Resources below).
Visit the Peabody Museum of Archaeology and Ethnology, just a little ways beyond the Sackler on the Harvard Campus. Housed inside a large non-descript brick building, this outstanding museum shows what a well-endowed university can do with its money. Here, you will find huge totem poles from the American Northwest, native canoes from the Polynesian Islands and exquisite hand-carved effigies from Central America. There is also a gallery space that sponsors changing exhibitions that are in some way connected to the world of archaeology and anthropology (see Resources below).
Visit the Harvard Museum of Science and Natural History. This museum is located under the same roof as the Peabody, so one ticket gets you into both places. This is a most fascinating place with an extraordinary collection of glass flowers, meteorites, brilliantly-colored minerals and an extensive array of stuffed animals from all over the world (see Resources below).
Head over to the MIT campus, which is near the river and check out the MIT Museum (web.mit.edu/museum). This institution has wonderful collection of holographic images and a permanent exhibition of sculpture that blurs the line between art and science.
Visit the List Visual Arts Center (listart.mit.edu/), also located on the campus of MIT. This museum is a great place to take a look at the high-tech side of visual art.