Hi Jimmy
About the luggages, there are luggage compartment in the Yokohama train station, however you need to pay the charges for about 200-400 Japanese yen for one compartment ( I don't know how big is your luggage.)
Which Tokyo airport are you going? (the Haneda airport or Narita airport)
The Haneda airport is within the Tokyo City and the Narita airport is quite from Tokyo City ( Located at Chiba perfecture, Narita City) If you are going to Haneda airport, there are direct train from Yokohama station. You can just takes KEIKYU LINE and it takes you about 20 to 25 mins to reach Haneda Airport. Please check with the train station personnel for train time table.Charges is about 478 Japanese Yen, 3 trains in every hours
For Narita airport, you can takes a Limousine Bus from Yokohama Station, from the YCAT terminal, about 3600 Japanese Yen, The bus departs every 30 minutes
I don't know how many hours do you have, but I would suggest you better not to go too far if you are not familiar with Tokyo and Yokohama.
If you want to move around Yokohama, after you put your luggages in the luggage compartment, you can take a train to " Sakuragicho" station, there is a amusement park which you will be able to have a view at the skycraper in Yokohama and the city view if you walks around the Yamashita Park, Chinatown nearby Yamashita park. If you have a 3 or 4 hours short time.
Or if you have 8 or 12 hours, then you can take a train toward Oshiage or Aoto terminal station from Yokohama with Keikyu Line connecting to Keisei Line.
On the way, you can drop at the following train station for the tourist attraction:
1)Â Shinagawa station-Â Giant Aquarium park
2) Higashi Ginza- Most expensive shopping, you can also walk from this station to the Imperial Palace toward Yurakucho Station.
3)Â Nihonbashi- The stock transaction area in Tokyo. train station
4)Â Asakusa -Â Â fanous tourist attraction Sensoji Temple, nakatori is a shopping lane in front of the temple where you can buy some Japanese gift
In order to come back to Yokohama station, remember to walk back to the same station when you alight from, because you can takes the train back to Yokohama station. Also, if you are coming back in the eveing around 5pm to 7pm, the train and train station will have a lot of peope coming back from Tokyo to Yokohama, if possible try to avoid taking the evening train.
If possible, try not to take a taxi, because it is expensive, also sometime you may catch up with a traffic jam.your may miss your flight.
Anyway, if you have problem with the train coming to Yokohama, You can takes a taxi to Shinagawa station, then you take a train to Yokohama, Shinagawa is a train station which we use to tramsit train to Yokohama using Keikyu line and JR LIne.
Alway reserved some spare time, for unexpected event happening on the way back to Yokohama.
Before moving around from Yokohama, go to the Tourist helpdesk to get some information, so that you can plan where you are going and how you are coming back.
I hope this help you.