It's hard to notice anything on this very large quadrangle other than the enormous Healy Hall (1897), a national historic landmark, whose high-set Flemish-Romanesque towers loom over the neighborhood, and even the city. It is named after Patrick Healy, who had an impressive career of firsts: the first African-American president of a major U.S. university, the first African-American with a PhD, and the first African-American Jesuit priest. During the day you can wander inside the building to appreciate the interior—Gaston Hall at the north end of the third floor should be your main objective, as it is both beautiful and has hosted endless visits by foreign and domestic heads of state. In the summer, these visits are often free to the public and not very well attended, so you might be able to get in and talk foreign policy with a king or two. Check the university's events website.
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This quadrangle was the original land purchase upon the founding of the university. The chapel (1893) at the south end, beautiful inside and out, is best known to the world for its role in The Exorcist, where the priests discovered the defaced statue of the Virgin Mary. The oldest building on the quad is Old North (1795) on the north side, from which Abraham Lincoln gave his speech in 1861 to Union soldiers stationed here. The best time to visit is undoubtedly at the end of the cherry blossom season, when the petals are beginning to fall throughout the quad.
Made famous by the 1973 horror movie, the "Exorcist Steps" run between Prospect and M St just west of where the Key Bridge deposits people into D.C. In addition to grisly ends to men and devils, the steps are popular among Georgetown students looking for a serious workout during their daily jog along the Potomac.
The bridge opened in 1889 and was used to transport boats between the C&O and Alexandria canals. The bridge was demolished in 1933, after the construction of the Key Bridge and the closing of the canals. Now, it is a grassy, peaceful area with great views of the Key Bridge and some unique graffiti!
A park on what used to be a reservoir, the hilltop is now a great place to get a view of Georgetown University.
Built in 1796 as a neighborhood pub, the City Tavern is the oldest commercial structure in the city, and the second oldest building following the Old Stone House. The interior is a beautiful trip back to the 18th century, but it is closed to the public, except for private event bookings.
A stately mansion built in 1815 by the son of the first mayor of Georgetown, and the step-granddaughter of one George Washington. The manor hosts permanent exhibits of 18-19th century American furnishings, as well as a large collections of items owned by George and Martha Washington. The gardens in the back are lovely, and can be accessed separately from the mansion for $3.