Asakusa is a great place to visit. The Sensoji Temple is beautiful, lots of traditional shops and restaurants. Even when the shops are closed it’s fun to walk around, because the street lanterns and the temple will be lit up which creates an amazing atmosphere. There are also restaurants which stay open until late and for some late night shopping you can visit the Don Quijote building around the corner.
Don Quijote (in English): http://www.donki.com/en/