Very little around MIT campus and Kendall Square is older than the Great Dome (the cap to building 10). It is modeled after the Memorial Library at Columbia University, which, in turn, is modeled after the Pantheon in Rome. During World War II, it was ordered capped with concrete as a security precaution, but the lovely glass skylight was installed again in 2013.
Over the years, the dome has been the the site of many terrific Hacks, as the pranks at MIT are known. The best Hack on the Dome was probably the 1994 assemblage of a police car with flashing lights on top of the dome. The cop car, painted meticulously to look like an MIT cruiser, was numbered pi, and the license plate said IHTFP, which is MIT’s unofficial slogan, though no one knows why. (I Hate to Fail Physics?) Also worth Googling is the image of when the dome was decorated to resemble R2-D2 from Star Wars.
Running through the Great Dome is in the Infinite Corridor. It is a 825 foot hallway running through several buildings at MIT. To get from east campus to west campus, you are going to want to take this corridor, as it is the most direct indoor route. Be careful though, the corridor is known for being like the streets of Boston–heavily congested.

Sources:
http://www.technologyreview.com/article/513156/mits-great-dome-gets-a-facelift/
http://constructoragc.construction.com/mag/2010/Mar-Apr/1003-MITDome.asp
http://hacks.mit.edu/Hacks/by_location/great_dome.html