Buy a day ticket for the Akai Kutsu bus at Sakuragi-cho. The Akai Kutsu, or "red shoes," bus is a tourist stop bus operated by the city of Yokohama just for visitors. It will take you to spots of interest to casual visitors of Yokohama. As of 2010, a day pass for this bus costs 300 yen, or the equivalent of a little more than $3.50. You can get on and off as many times as you like.
Get off the bus at the Nihon Oodori stop. From the bus stop, you can see several museums within walking distance. Choose from among seeing the Yokohama Museum of EurAsian Cultures, the Newspaper Museum, the Silk Museum, Isezaki-cho or the Museum of Yokohama Urban History. You can spend the entire morning --- or the entire day, if you love museums --- wandering around the museums that appeal most to you.
Hop back on the red shoes bus and take it to Chukagai, Yokohama's Chinatown. Make note of where you got off the bus so you don't get lost, and explore Chukagai's streets and alleyways. Here you'll find Chinese merchants selling all sorts of gifts, including silks and fine pottery. You'll also find plenty of restaurants and street vendors. Perhaps by this point in your visit to Japan you've noticed that eating can be expensive. Chukagai is your opportunity to try a bounty of Chinese dishes, dumplings, treats and snacks for very little yen. This is definitely a good place for you to stop for lunch on your Yokohama tour.
Find your way back to the bus and ride it to the end of the line, Minato-no-Mieru Oka Koen. This is the Harbor View Park. From this park, you can see the Yokohama Port and the Yokohama Bay Bridge. Stroll toward Motomachi, the first settlement of foreigners. In this neighborhood, you can find a few old foreign houses. You can also find several upscale shops and cafes. Walk to the end of Motomachi and get back on the bus headed back in the other direction toward Sakuragi-cho.
Get off the bus at the next stop, the Marine Tower. The tower was build in 1961 and is one of the tallest inland lighthouses in the world. If you pay a small entrance fee, you can visit the observation deck from which you can view the entire city. From the tower, you can see the Hikawa-maru, the only mainstream Japanese passenger liner to survive World War II. You can't take a ride on the Hikawa-maru, but you can climb aboard and have a beer in the beer garden during summertime.
Walk from the Hikawa-maru toward the Osanbashi Pier. The pier will be easy to recognize, because it looks like something out of Star Trek. The rooftop of the pier is open to the public 24 hours a day and you can climb up and see visiting ships close-up for free.
Take the Akai Kutsu back to Sakuragi-cho and have some fun in the Noge neighborhood. This is a popular nightlife spot in Yokohama, where you'll find a wide variety of dining and drinking options.