Wow, thanks guys! I'm loving all these suggestions!
@purpleinopp thanks for so many suggestions! I'm going to look those up! The cardboard idea! Woah! Love that.
@Peggy8b @brieth95 I also have ivy that grows everywhere in my yard. It does prevent unwanted weeds from growing and I pull it up if it starts to creep into places I don't want. It looks nice against the old moss- covered stone tiers of the garden.
The one I really struggle with is the trumpet vine and I've written a post solely about my struggle with that. This year, though, I think I'm just gonna let it grow and see what happens. I can't fight it anymore.