Traveled via Shinkansen (Bullet train) from Osaka to Tokyo. Highly recommend experiencing Shinkansen at least once. You see towns fly by you like its nothing and a very smooth and short ride (3 hours). Ticket was average priced around $135 for one way.
Days 6 - 11: Arrived and checked in hostel (Unplan Shinjuku). Shinjuku is a very central and happening area. Its also very expensive area to stay in therefore decided to sacrifice comfort for location by staying at a hostel. The hostel was new and recently renovated i believe. Would recommend a stay overall. Walked to Shinjuku Gyoen garden which was nearby. Great park for a relaxing afternoon. Food can easily be found on google depnding on what you are craving. Afuri ramen was one of the best i tried. So many options for food, hard to decide. Make sure to try gyoza, ramen udon, yakitori, curry and sushi. The city is very crowded but also very clean which is easily noticeble. Heaven for people into anime and gaming. Some of the attractions i visited were Tokyo skytree, Odaiba, Roppongi for nightlife, National government building for views of the city, Ginza district for fancy shopping, Shibuya crossing just to check it out. One thing is missed was to experience an onsen. This is one of the most recommend things but just did not have enough time. There is a popular onsen in Odaiba called Oedo onsen which i heard is good. Overall 5 - 6 days is good amount of time to see the main attactions. Tokyo is a very large and spread out city where you can spend weeks easliy.