Only 4 days? You should start with Tokyo.
I would highly recommend Sunroute Plaza Shinjuku hotel (
http://goo.gl/maps/GXoYx), clean, convenient, and there's a direct bus to/from the airport. Also everything you want to buy in Tokyo, you can find in Shinjuku or nearby Harajuku, Omotesando, Shibuya.
Shopping: Takashimaya Times Square and Tokyu Hands (in the same building) in Shinjuku. Tokyu Hands has all kinds of things you never thought you need, I can spend hours there. Harajuku has Laforet, which is an entire building full of women's clothes, and little streets full of quirky shops. Shibuya has 109, which is an even bigger building full of women's clothes (shibuya109.jp/en/top). Mostly local brands. Roppongi Hills is also quite interesting, the Diesel brand in Japan somehow has better (and different) stuff than the shop here, maybe because their Japan buyer has better taste in fashion?
Roppongi Hills has more international brands.
Sightseeing: I would highly recommend Meiji Jingu Shrine in Harajuku (you can go shopping after). It's probably one of the oldest and largest shrines in Tokyo, and still being used for wedding ceremonies, usually there are a few during the day. It's very tranquil and the surrounding forested area is beautiful.
You should also do a day trip or overnight trip to Hakone, up in the mountains. It's beautiful and on a very clear day you can see Mount Fuji. Try the hot springs!
Eating - I've never had a bad meal in Japan so you should be OK even if you don't know what you're eating. My favorite places:
Satou Steakhouse in Kichijoji - Best steak I've ever had. Place is a hole in the wall, but the beef OMG. They use the famous beef from Matsuzaka, worth every penny (and it's a pretty penny) I'd go for the highest-grade beef.
http://goo.gl/maps/EKZ22
Gogyo ramen - My favorite ramen place, that happens to also be a bar. It's opposite Hardy's Barracks in Roppongi, near Roppongi Hills. PM me if you need a map with walking directions/subway exit number.
http://goo.gl/maps/UYSQH. Google Travelling Hungryboy's blog for the review.
Maisen tonkatsu - famous for the deep-fried breaded pork chops. Its Harajuku location was formerly a traditional bath house, charming.
http://goo.gl/maps/zrOF3
When are you going? June, Jul are very hot, August is hot and crazy rainy in Tokyo.