Hi there!
Right now you can purchase the Monstrous Mask from the Grocery Store.
Regarding the park's cave, there's only that entrance, currently it's a small dungeon yeah, and the "door" you see in the minimap is kind of saved for an event that will come in the future.
You can also try the sewers dungeon at Downtown, that one is randomly generated everytime you enter so there should be more plenty of loot there ;)
Thanks for playing!