Lucky you

I'm going in March for a few days and was there on NYE (and visited 4 times before that... I like the place..)
As have been suggested, the Old Town, Kazimierz (Jewish Q), a day trip to Auschwitz and the Wieliczka Salt Mines too.
What I haven't seen suggested so far:
If in Kazimierz, you must take a few hours over the southern side of the Wisla, and visit the Podgorze district. This is where the Krakow Ghetto was during WW2. If you take the eastern bridge, you arrive in Ghetto Heros Square which has a big public art work, and loads of info on the surround area, including a trail map to see different sights, including sections of the Ghetto wall.
A couple of minutes to the east of here is Schindler's Factory, which has been under going restoration, but I believe is now partly open.
If you are feeling adventurous, you can also visit the Plaszow concentration camp, which was made famous by the Schindler's List film. The actual camp doesn't exist anymore, but the area in which it was is preserved, and has various small memorials dotted around it, and a large Soviet built memorial at the top end. A large cross on the way up to this memorial marks the spot where the Nazis dug up thousands of bodies, only to then cremate them (as seen in Schindler's List too).
Myself and the Mrs spent a good couple of hours wandering around, it's a very thought provoking place - almost as much as Auschwitz, when you consider how close it is to the city.
Between Podgorze and Plaszow CC, there is also a large public mound - I forget it's name.. but you can't miss it, it gives fantastic views of Krakow in good weather.
There is a large, disused quarry next door too, which is where Schindler's List was actually filmed.
Nowa Huta is one place I haven't managed to venture yet.. but if you are interested in the Communist era, this place is it. Built by Stalin for the residents of Krakow, at the centre of which is (typically) a massive steel mill.