Touch the Japanese culture when you first arrive in Tokyo. I think just by talking to airport staff, you can feel the hospitality of Japan. And start from eating! Only by searching your favorite food such as sushi, ramen, sukiyaki, wagashi, etc., with your smartphone,(example:sushi tokyo Foreigner) you can find various restaurants. I recommend "Hato Bus" as well! Hato Bus will take you to many tourist spots.
What kind of experience would you like to have?If you want to popular experiences, I think good to buy and follow popular guide book.
I want to you experience and feel various culture in Japan.
Have a nice trip!
If you like otaku culture, you should to go to Akihabara or Nakano broard way. The area is specialize for otaku culture. Are shopping in Kotobukiya, maid cafe, arcades, new things to you?
Speaking of food, soba, Tendon (Tempura), Dojo-Nabe (loaches hot pot), Fukagawa-Meshi (clam rice), Monjayaki, etc., would be my recommendation. There are good restaurants around Ueno or Kanda, close to Akihabara.
In Ueno, there are huge museums, shrine, and park so if you want to feel Japanese culture, you will enjoy the area very much.
Also, challenging to Japanese Izakaya might be fun. You can taste Japanese dishes and alcoholic drinks, and feel the atmosphere of Japan.