Krakow is incredible. I've been twice, both times as a single (female) parent, first time with my daughter and disabled son, second time just my daughter. Both time I've felt incredibly safe. We've walked and publiced transported all over Krakow. I'm going back somewhen... soon... i love it
Consider staying in or on the (edge of the old town. All the transport centres around where the old walls were. Ideally you want somewhere on the walls park or within a road if you are considering any trips outside with hotel pick up (often they can't go in to the old town). Can highly recommend "the old town Great Polonia" (great polonia is a chain so make sure you know which one you book!), (although I'd strike out independently for breakfast). Only a few roads away from the main square, short walk to the station and accessible for the taxis. And cheap when we went
Auschwitz is very easy on a day tour. However you can go independently. You need to book Auschwitz ahead directly and there is a bus that used to run from the station in krakow straight there. The return journey was quicker but we had to change bus. It was significantly cheaper this way and we got there early so missed much of the crowds. It was definitely more atmospheric before the treadmill of tour groups arrived. The audioguide gave you everything the tour groups did and for us travelling independently had the advantage that when we had had truly had enough we could leave.
Consider doing a tour to zakopane mountains, wooden village and thermal spa. Can highly recommend the Termy Bukovina. Such a spectacular trip weve done it twice. However do check which Termy they are taking you to. I think most the options are ok but there is one thermal spa that is little more that a local leisure centre. The Bukovina is truly spectacular and so relaxing, especially if you've done Auschwitz previous day/earlier in the week. We did this as a private tour both time and whilst an expensive treat it is utterly unforgettable.
Google maps works fantastic out there for planning routes. Both times we got a private transfer from the airport to get us into krakow as quickly as possible but took a bus back. Very safe and easy.
There is so much to see. The museums and castle are all fascinating but Some of the random museums on the outskirts are well worth taking the tram out to look, especially as often they are in a bundle deal with the underground museum under tge square. Walk out to some of the more "local" milk bars for really cheap harty food and a uniquie experience, have google translate to hand! Less barginous we did the communist tour in a Trabant last time and that was also fantastic. I haven't yet got round to the salt mills.
Eat at the Black Duck at least once. You have to book it though. Not the cheapest meal, but not the most expensive either and gorgeous traditional food. We also went back regularly to Restauracja Sukiennice in the town square for, bargainous snitzel and other specials, fabulous puddings (strudel) and cherry brandy.
Yes the horse and carriage from the main square are a tourist trap. BUT wow!! DDs turned 18 while we were there, it was a surprise birthday treat. But i wil never ever forget it, there literally is no way better to see the town.
Wear shoes with good grip if you go during snow. NOTHING stops when it snows, but it can be a bit slippy.