I think major sights are below:
Asakusa - famous Sensoji Temple, Nakamise Dori. As it was center of the commerce from Edo period, lots of hubored year old restaurants. Soba, tempura, sukiyaki.
Ueno - Large park, zoo, great museums. Ameyoko is fun street to enjoy street food.
Oshiage - Tokyo Sky Tree, old meets new, great view of Sakura along Sumida river
Shinjuku, Shibuya - center of modern culture, shopping, eating out, nightlife, lots of Izakaya.
Harajuku - kawaii fashion, center of teenage culture of Japan.
Akihabara - electric city, otaku, manga and anime, maid cafe.
Tsukiji & Ginza - World's greatest fish market, high-end shopping, Tokyo's highest class restaurants.
Mitaka & Kichijoji - Ghibli museum, beautiful park
Sugamo & Komagome - beauntidily Japanese garden Rikugien, shopping street for elders.
There are lots more attractions according to your interests! I think Tokyo is a city to stay for several nights and best way to enjoy the city is taking time to walk around, interact with locals :)