I'd recommend rather Kazimierz district or Krowodrza, both are walking distance from the Main Market Sq. and much more prestigeous too.
Kazimierz is definately more prestigious and the flats there are brilliant. But, if you don't know the place, you will more than likely end up paying through the nose for a flat there. It's extorsionate!
As for Krowodrza, I quite liked living there...it was a nice area, but I wouldnt say it was walking distance from the main square. I mean you could walk it, but it would be quite a long walk. However the trams/buses are frequent, the only problem is that late at night the night bus is only once an hour which can be a bit of a nightmare.