Your two woodpiles are among the neatest I have seen in recent years. You could install an outdoor curtain and rod along the ceiling. But really. the woodpiles look quite nice just as they are.

Need more photos since we have no idea where that planted bed and channel in the grass are coming from. Can't fully see the trees on each side. Also take a photo facing the front door. From the limited view, a deep bed, starting with the tree on the right with layered shrubbery of different heights would enhance your house.

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Your home was not designed to accept shutters. I would remove those first and pressure wash the brick of the home.

Seconding Beverly on the shutters. Although you just asked about landscaping, designers consider curb appeal, which includes the look of the house as well as landscaping. Again, we have very little to go on, so send more photos.

Is it possible to integrate both woodpiles into one? I would probably fill the area between the posts and pile the wood higher. It would become its own screen and give you more room on the slab for your table. If you then want to hide the pile, you would only have to screen one section, not two. A curtain as someone suggested, or even an actual screen, but these would limit your access to the pile from the patio, if you need that. They would have to be made with openable doors somehow.

Or maybe a roll down shade that can be rolled up out of the way during the cold season when you don't use the patio, but need access to the wood?