Plenty of hiking trails and nature walks that I've lived near; these were free and pleasant.

Maybe redundant with university campuses: free museums (especially art and history).

I've found several game stores that host game-hours at off-peak times. These have all been free and quite pleasant.

I'll note that Malls may not work for youth anymore, I've seen a few that outright ban unaccompanied teens (which is a shame imo).