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)
Read our famous and comprehensive guide to everything you need to know before vistiing Kraków!