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).