Looking on the internet deeply has found these results:

headed into the park is the most popular phrase on the web.

headed for the park 17,230,000 results on the web	headed into the park 17,720,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
Suspect's headed west on park row. Actually, we were just headed to the park. We lost them in the park headed south. Ambrose is headed to Verdugo Park. She pushed me away, scratched me, and then headed into the park. Searching the nearest surveillance cams, we got a black '09 Chevy Malibu possibly headed from the park at 4:30 a.m. Fredericks seems to be headed for the national park. Four nights ago, Sam Alcott headed to the park, just like Simms.	She pushed me away, scratched me, and then headed into the park. Four nights ago, Sam Alcott headed to the park, just like Simms. Actually, we were just headed to the park. Ambrose is headed to Verdugo Park. Searching the nearest surveillance cams, we got a black '09 Chevy Malibu possibly headed from the park at 4:30 a.m. She's headed into Vista Hermosa Park. We lost them in the park headed south. Suspect's headed west on park row.

headed for the park

17,230,000 results on the web

headed into the park

17,720,000 results on the web

More popular!

Suspect's headed west on park row.
Actually, we were just headed to the park.
We lost them in the park headed south.
Ambrose is headed to Verdugo Park.
She pushed me away, scratched me, and then headed into the park.
Searching the nearest surveillance cams, we got a black '09 Chevy Malibu possibly headed from the park at 4:30 a.m.
Fredericks seems to be headed for the national park.
Four nights ago, Sam Alcott headed to the park, just like Simms.

She pushed me away, scratched me, and then headed into the park.
Four nights ago, Sam Alcott headed to the park, just like Simms.
Actually, we were just headed to the park.
Ambrose is headed to Verdugo Park.
Searching the nearest surveillance cams, we got a black '09 Chevy Malibu possibly headed from the park at 4:30 a.m.
She's headed into Vista Hermosa Park.
We lost them in the park headed south.
Suspect's headed west on park row.