I visited the Tatra mountains over the summer from the Polish side. With beautiful views and great weather, the Tatras are a prime location for trail running.
One of the good things about the Tatra National Park is that it has many trails with different levels of difficulty. The park requires a small entry fee at the main entry points, around 2€ per person.
These trails are very well marked, so there is little risk of getting lost. The trails can vary, from the flat and wide dirt trail to the very technical and steep mountain trail. Contrary to what intuition may tell you, the color of the trail marker has no relation to its difficulty.
If the weather is good, you may come across large crowds on the main, flatter, trails (even during pandemics). However, most of the other trails are empty, visited only by other avid runners and hikers.
I met a local trail runner on my way back home. He mentioned that the best time to run was at the beginning of autumn. At that time of the year, the mountains are still not covered in snow and the number of visitors is much smaller.
Sites like Komoot may give you an idea of some trails that can be done. But this is by no means a representation of the vast number of trails there exists in the area. My recommendation would be to go old school: buy a map. They are available for a fee at the main entry points of the park.
