Kyoto has a very cool old world vibe to it so it can inspirational to visit some of the shrines and cultural sites.
In Tokyo, it depends on what you want. Akihabara for your nerdy anime and electronics stuff. Asakusa is nearby and has a really cool old shrine. If you go on Sunday, you might see Shrine people dealing with the Cosplayers.
Shibuya and Harajuku for fashion. Sunday you might seem some of the more crazy fashion. Make sure to hit the Shibuya train station to see the famous crosswalk and Hachiko statue.
Nagano and Ikebokuro are great places to shop? Nagano has a really cool mall that has a lot of old collectables.
Really, when I was there years ago, Sunday is the day when young people are off so if you want to see crazy costumes and stuff so check around and you might see Lolitas, cosplayers, or the guys with the kick ass pompadours.
Also shrines are a must.