Learn Polish: Pójdę pobiegać w parku obok szkoły. - I will go run for a while in the park next to the school.

The prefix po- adds a delimitative meaning, showing that you will do the action for a limited, relaxed amount of time. Instead of just indicating the general activity of running (biegać), pobiegać specifically means you will run for a while and then finish.

Why is po- added to the multidirectional verb biegać rather than the unidirectional biec?

When you add po- to a unidirectional verb of motion like biec, it usually creates a perfective verb meaning to start moving or to run to a specific destination (pobiec). To get the delimitative meaning of doing the activity casually for a while, you must attach po- to the multidirectional verb biegać.

Both pójdę and pobiegać are perfective. Is it common to pair them like this?

Yes, it is very common when expressing purpose. Pójdę indicates that the trip itself will be a completed action in the future. The perfective infinitive pobiegać shows that the short running session is the purpose of that trip, and that this session will also be a completed, bounded event.

Why is it w parku (locative) if the sentence uses a verb of motion (pójdę)?