There are actually many interesting things to see and do in Yokohama!
Firstly, you guessed it - you should rent a bicycle or sign up for a bike tour so you can cover a lot of ground easily and thus make the most of your day! A bicycle is probably the best way to get a good feel for a city when you don`t have so much time.
Three things to do:
Explore Minato Mirai - this is the ultra modern part of the city. Start by shopping and eating at Queens East and Landmark Tower, then ride the roller coaster or enormous Ferris Wheel in "Cosmoworld". As the sun is going down walk toward the waterfront and enjoy the amazing views (and more shopping) at World Porter and Aka Renga (Red Brick Warehouse). Aka Renga are two old warehouses that have been converted to a great shopping and dining space. There are usually events like concerts here as well as seasonal stuff like a Summer beach park, Ice skating in the winter and a great outdoor "Octoberfest" in Autumn.
Yamashita Park and Chinatown - Yamashita is a beautiful old waterfront park that is known locally as Yokohama`s front yard. A great place for a stroll, a ride or to take a break. Not far, from the park is Chukagai AKA Chinatown. Here you should just go with the flow and enjoy the experience of wandering and getting lost amongst the colorful, confusing but always interesting sights and sounds and smells of the area.
Kannai and Noge - Kannai, is just to the west of Chinatown and near to Yokohama Baseball Stadium. It is the cities entertainment area, full of restaurants, bars, hostess clubs and Jazz clubs. Noge is close to Sakuragicho Station, but is a more compact area of old streets and interesting casual restaurants. It`s where the residents go to unwind after work for an inexpensive good time. In Spring, the nearby Ookagawa River is definitely worth seeing when the Cherry Tree, which line it`s "banks" are in bloom. Saddling up to a seat at one of the stalls set up under the blossoms is a perfect way to end the day.