Enjoy walking around central Tokyo
I have never lived in Tokyo, but I love day trips there.
I would spend a few hours walking around Omotesando and Harajuku- interesting people watching and window shopping, great dining, shady streets, very international & trendy cafes
I also fell in love with walking around the Ginza on the weekend when they shut down the main streets to traffic and people sat in the middle of the road drinking and eating and mingling- it was fantastic! great shopping and people watching, dining and very trendy here too.
Into anime and electronics? Gotta hit Akihabara:
Head to Asakusa and see the nearby sights like the giant golden turd
I think Yokohama is also really fun- especially Chinatown or the Harbor area, shopping, amusement, etc... but probably not if you only have 1 day in Tokyo