You find a lot of interesting in the Whitechapel area. Spitalfields Market, Brick Lane, and Whitechapel Gallery are just around the corner. Take the tube to Aldgate East and the Gallery just a short walk from there. The London Art Centre is a great place for modern art and happenings, pointing in different directions.
Don’t forget to have a curry. In the area, some of London’s best Indian and Pakistani restaurants are situated.