Krakow is a small city with a big population, and lots of parks.
The most popular is Planty Park, which circles the old town area. It replaced the old city walls in the early 1820s. There is a nice guide to walking through Planty Park here.
Another nice park and outdoors area that is close to the city center (10-15 min walk from square) is Blonia Park. It means 'Meadow' in Polish, and is a huge open area that is often full of runners and inline skaters (along the pavement/sidewalk). It is in the middle of the two football grounds - Cracovia's Stadium and Wisła Krakow's stadium.
Read about exploring the abandoned Liban Quarry (and ex Nazi labour work camp)