If you live in Kraków the city seems huge - but as tourists it seems very small. Almost all of the areas that tourists would want to visit are within walking distance.
There are two main areas - Old Town (green in the map below) and Kazimerz (yellow, on bottom right of map below).
Tourists tend to spend more time in the Old Town area (around the main market square), but Kazimierz is popular too.
The green area in the map below is where we would recommend people stay, if booking a hotel/hostel/apartment. An alternative could be in Kazimerz (bottom right of map, in yellow). The orange section is also a short walk to the main square, so is another option. We really would not recommend staying somewhere if it isn't on any of the highlighted areas of the map, as there are loads of hotels/apartments/hostels in the shaded area and you will have to walk a long distance or get trams/busses.
The white area in the middle (directly behind the big black 'Kraków' text) is the Old Town's Main Square.
Read about exploring the abandoned Liban Quarry (and ex Nazi labour work camp)