Walking north - or taking the #3 / #19 tram lines for two stops - from the "Policlinico" metro station (located right behind the city's "Sapienza" university) along viale Regina Margherita you'll cross via Nomentana. This is a quiet and elegant area; a wide boulevard with stately buildings. There are B&B 's in the area and it is a a nice refuge from the older, more dense central Rome. Locals call the district Nomentano even though via Nomentana seems to run farther northeast.

Besides the elegant 19th-century detached houses, this district has a few attractions to offer: for example, you could take a stroll at villa Torlonia. The so-called casino delle civette is an interesting example of Art Déco notable for its stained-glass windows; the casino nobile - that is, the main building of the complex and the first one you'll see upon entering - not only is a stately 19th-century manor (designed by Giuseppe Valadier; interesting marbles and frescoes inside) but was also Mussolini's official residence from 1929 to 1943; there's also a WW2-era bunker beneath the manor, which can be visited. False ruins, obelisks and a theatre ornate the rest of the park.

Right in front of villa Torlonia, there's the much less scenographic villa Paganini with its small ponds, making it an ideal place to rest your feet. 

Following the via Nomentana to the city centre (take the #90 trolleybus towards Termini station),  you'll come across a busy square with the imposing remains of the city walls as a backdrop. The impressive Porta Pia (that is, the city gate located in front of the square) was designed by Michelangelo himself and was the place from which the Italian troops entered Rome on September 20, 1870, thus ending the millenary rule of the Popes and completing the process of the Italian Unification. A monument, located right in the middle of the square, celebrates the soldiers (especially the Bersaglieri) who gave their lives for the cause.

You can also get off at the "Sant'Agnese - Annibaliano" Metro stop of the B1 branch of the "B" line (to get there, take any train towards "Conca d'Oro"): the unspoiled, touristically speaking, catacombs of Sant'Agnese and the mausoleum of Santa Costanza are located nearby.