I'm not familiar with Kyoto so here is my opinion about Tokyo:
Shinjuku has everything. Shopping, dining and drinking options, cafes, bars, etc. Many places are open until late so even though you come back to hotel after busy day, there still be options to eat in this area.
Shibuya is almost the same as Shinjuku, but Shibuya is more dedicated to youth culture. Shibuya is the center of the youth culture in Tokyo, lots of teenagers visit Shibuya after school or on weekends to have fun with their friends. Harajuku is also a walkable distance from Shibuya Hachiko.
Asakusa & Ueno:
Asakusa is where the famous Sensoji Temple (The temple with big red lantern) is located and Ueno has zoo and Ueno park. This district is more traditional comparing to other areas in Tokyo. You can find normal hotels and also ryokan in this district, although the number of ryokans are limited comparing to Kyoto and other areas.
Roppongi is where the luxury hotels are. Maybe not a strong option if you are traveling with your teenage son because the area's feature is night clubs. This is one of the "Foreigner" district so there may be lots of English friendly restaurants and bars.
Marunouchi (Tokyo Station):
This is another rather luxury area but more casual than Roppongi. Because it is close to Tokyo Station, it is easy to get on Shinkansen when you are going to Kyoto. Tokyo Station has many train lines both JR and metro so it is easy to move around within Tokyo and to outside of Tokyo. Tokyo Station's underground shopping mall is fun, there are souvenir shops and Pokemon, Ghibli, and other character goods shops too. There are many dining options in this area as well.