Por is the word for moving through, along or around a place:

• Estamos dando un paseo por el barrio. — We're taking a walk round the neighbourhood.
• Corro por el parque. — I go running in the park.
• Paso por la farmacia. — I'll drop into the pharmacy.

You already know it from por la mañana and por la tarde. It also means for when you thank someone: Gracias por el café. — Thanks for the coffee. And por never merges with the article: por el parque.

Three ways to go for a stroll: dar un paseo — to go for a walk; pasear — to stroll, to wander about; dar una vuelta — to go for a wander, a quick spin. ¿Damos una vuelta? — Shall we go for a wander?