I think they used that same park a lot. I think it was in Those Love Pangs where the tramp sees woman pull money outta her delicate boots and insists the buddy accepts ...all the while smooching his face. The tramp just rolls his eyes sitting on the park bench under the tree just behind the couple....like ..."why not me!!!"
It is my understanding that "In the Park" was filmed entirely on location at Golden Gate Park in San Francisco. The only other of Charlie's productions I'm aware of where scenes were filmed in and around this park is "A Jitney Elopement" which immediately followed during his short time working at the Essanay Studios in Niles, CA.