There are some good parks for running off Piotrkowska St., particularly toward the southern end. Just south of al. Adama Mickiewicza, head west for 0.5 km to the extensive Prince Józef Poniatowski Park, which has numerous lovely paths for running. At the Central Museum of Textiles, there’s the small Reymont Park. And at the southern end of Piotrkowska, you can do a ~1 km loop around Legionów Park, with its magnolia trees, gardens, & 19th-century villa.