With 4 months, you'll have plenty of time to explore. The main Yokohama area is somewhat a family-ish area (lots of outdoor activities, shopping, there's the ferris wheel, etc). The international pier is a beautiful place, and it's fun to just hang out there.
Check out the Red Brick building, there are a few nice bars and restaurants there. There's also the sky restaurant at the bay bridge, though it's more of an upscale date spot. I don't know more specifics about nightlife around Yokohama, but don't forget you can just take the Keihin line from Yokohama station right into Tokyo (and transfer at Shinagawa station to the Yamanote line to get to any of the major areas).
I need to spend a little more time in Yokohama the next time I visit [December]. Bento.com has a reasonable selection of pubs and bars in Yokohama. Thrash Zone sounds especially intriguing. :surprised:
Do remember that now Yokohama is served by not only the JR and the Keikyu Line (which is through-routed onto the Toei Asakusa Line), but also the Tokyu Minato Mirai Line, which runs direct from downtown Yokohama to Shibuya. :happy: (Fare: ¥460)