Depending on where you live, interesting places could be pretty close. When I was new in my city, I sometimes took a tram or bus to the most remote stop, and just picked a direction to walk from there. Obviously exercise some common sense, and it won't be the "scenic" route for the bs social media pictures, but it can be a pretty rewarding adventure.

Yeah that's the caveat, you just have to be there but the "being there" part is most likely an expensive one. And the best trail with great view is usually very much in the middle of nowhere, so very unlikely there will be a public transport going there. Still, there's no reason for no public transport going to the green space within the city.