Tokyo is amazing, a definite mixture of old and new and surprisingly easy to get around so I guess-
1/ The train system-it is fantastic and so easy to navigate around the city, it is clean, quiet and fantastically efficient, which means that you get to see so much more of this amazing city. Don't be afraid of what you see on videos....yes it can be squishy and crowded but it runs so smoothly you honestly don't realise that.
2/Sensoji Temple or Asakusa Kannon Temple
is Tokyo's oldest temple, and is easy to get to, from the Asakusa station on the Ginza line. With it's Main Hall and five storied pagoda it draws lots of visitors and worshippers all year. For those that like to shop, Nakamise, the shopping street leading to or from the temple area is full of souvenir shops and food shops.
3/Food and shopping-not sure if this is just for Tokyo but all of Japan-there weren't many places that we didn't like eating from the pork buns at the 7-11 to the pancakes in Takeshita St to the many different restaurants that we went to, and all the snacks we ate the food was amazing. A great eating area was Ebisu,one station up from Shibuya station on the Yamonote line
(which was great for us as our main base was the Tokyo Plaza Hotel on the Yamanote line). Ebisu had so many little restaurants (check the gallery for photos as there are a few there) that it was hard to choose from, but would have kept you eating for months I think. Shopping is great and not nearly as expensive as you would think, from clothes and souvenirs in Takeshita St to Shibuya and Shinjuku with it's many stores. Whatever you are looking for you will find in Tokyo and if you check this shopping guide it will give you more detailed information about the best places to shop in Tokyo.
4/ The Meiji Shrine and Yoyogi Park, which is an oasis in the middle of a busy city. We found out after the fact that the easiest way to get to the park was from Harajuku Station but we came from the other side at the Meiji-jingu-mae Station on the Chiyoda and Fukutoshin Subway Lines. (Going this way was pretty good though as it gave us a chance to explore more). There are lots of walking paths around the park, and you enter the park through a large wooden torrii gate at either end of the park which gives a great photo opportunity. There are many buildings to see within the complex so I would allow plenty of time to explore them all.
5/Observation towers-yes I know it's not for everyone but I love seeing a city from above and with the Tokyo Tower it's striking red, with similarities to the Eiffel Tower which stands out on the Tokyo skyline. Entry to the main observatory of the Tokyo Tower is 900yen approx $10 AU and for both decks which we did was 1600 yen approx $16 AU) and the Skytree, with it's neon lights and amazing shopping centre which even had me shopping
and the custard banana cakes yummy(There are two prices again, for the Tembo Skydeck the lower level observation deck which is 2060 yen $20.60 yen and the upper level Tembo Galleria which is and extra 1030 yen $10.30 AU.) Again not everybody's thing but I love seeing the city from above and I think that gives you a great perspective of how huge a city can be.
6/Getting lost in Tokyo-there are so many things to see that getting lost is really not a concern (you usually find your way back to a train station somewhere) and just walking around the streets away from the touristy areas of Tokyo to see how life is really lived. (Heads up-get your hotel written in kanji so if you do get REALLY lost you can find a taxi to take you back to your hotel-not all Japanese people speak or read English so having your address written out for you can be an advantage.)
7/This isn't quite Tokyo as it is on the outskirts, one hour from Tokyo station, but I love Narita, with Shinshoji Temple and the Omotesando
with it's lovely little shops and amazing scents and smells. If you are ever transiting through Tokyo and don't get the chance to actually get into the city itself take the time to explore Narita.