For Tokyo. Must go places
1) Tsukiji Fish market, go there at 4 to 5am, the whole market shuts down by 9am. Its an experience honestly. After that you can go have fresh sashimi and sushi at the many restaurants at the market. Note however that it is closed on certain wednesdays. Just go to any restaurant in the city that has fish on their menu and ask them to check for you. The owner would have a Tsukiji schedule book
2) Shinjuku and Kabukicho area
Go at night to the Kabukicho area, its the red light district of Tokyo, but dont worry, no girls in the streets kind of thing. Its more to see the sights which include men dressed in suits and looking like J Pop idols on the streets trying to hustle girls to "Girl Bars" (Their version of nightclubs for girls) and just taking in the sights.
3) Shibuya area
Go and suck in the atmosphere and of course look at the famous Shibuya crossing. Lots of interesting shops here to see
4) Harajuku, Omentosado Hill
The fashion crazy locale of Tokyo, from high end LV to lower end far east square type of clothes. Main attraction is the students all dressed up and looking like they walked out of a magazine. Also if cosplayers are a plently here
5) Asakusa Temple
Lots of things to buy as there is a big market in front of the temple and good tempura restaurants around.
6) Roppongi Hills
There are a few art galleries here which are interesting and its the party scene of Tokyo
Lots if boutique fashion shops. A more upmarket version of our club street and much bigger too. The iconic Prada building is located here.
The sim lim of Tokyo only difference is that it is the size of orchard road. Lots of gadgets and also if you are into toys... u will go mad... all sorts of toys abound.
The above 8 are just some of the places to go.. honestly there are tons of places more to explore. Odaiba, Ginza, and some other areas not on the tourist map. But then for 5days. This should be enough for you. Note that on your last day, unless you have a night flight, u will most likely have to leave for the airport at 10 to 11am. 1 hour to get there, 2 hours for check in and other stuff and then spend rest of time at the airport shops. So dont plan anything major on the last day. Also dont go past boarding until u are almost going to board the plane. At Narita, unlike Singapore airport, the shops are outside the boarding gates not inside, so once you pass boarding gate,s its a dead town inside....