Krakow is centered around the Old Town and its magnificent market square. It's the largest medieval town square in Europe. Both tourists and locals come to the market square with its many restaurants and bars. While I was visiting, the Christmas market was active which meant the square was particularly lively in the evenings. Old Town has many beautiful historical buildings as well as a plethora of cathedrals.
Kazimierz is the second historic district on the toursit circuit and, like Old Town, it's not just for tourists. Kazimierz is both the historic Jewish quarter and the modern trendy district with many art galleries, offbeat shops and hip restaurants. Walking the Kazimierz during the day, the signs of its prior existence as the Jewish quarter are everywhere which is a poignant reminder of the tradegy of the Holocast.