Beit Hakerem is a lovely neighbourhood, close to Hebrew University's Givat Ram campus, the Shaarei Tzedek hospital and Har Hertzl.
The name itself means "House of the Vinyard" and is an old town, having been established in 1922 as a separate "Garden City", isolated from Jerusalem by surrounding open land, though these days, the city of Jerusalem has grown and expanded to encompass Beit HaKerem. (not being part of Jerusalem is the reason that several of the older buildings in the area aren't built from Jerusalem stone)
Israel's Antiquities Authority has also undertaken excavations there with finds dating the neighbourhood back to the First and Second Temple periods.
Beit HaKerem has fantastic transport links, being located on the current (and only) line of the light rail and close to the Begin Highway (one of the best ways to move north-south within the city and that connects to the "1", the main highway out of Jerusalem).