Hi!

When buying outdoor fabrics, you want to always focus on the durability making note of its ability to withstand the elements, its fade resistance and water resistance. Polyester and Olefin are the best fabrics for outdoor curtains, they are durable and medium weight. There are also fabrics with stain resistant properties. You can buy exterior curtain rods from most home improvement stores, amazon.com, Walmart.com ect. The brackets you choose depend on your personal style, width between post and the height of your pergola.

For your backyard layout I would put corner curtains between you and your neighbor near the gate, the curtains should be in the shape of a V from each post rear the gate, depending on your family and usage you could also put a curtain on the post near the pool.

-Alley

Start with the two by the fence and if it looks unbalanced, add two more. Ideally, it's a rod or wooden dowel with curtains with grommets and tie backs. Search for outdoor curtain with grommet. If it's not functional, you probably don't need Sunbrella fabric but you'll want something washable.

Closeup of the rod and grommet treatment

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You can do as the picture above just where it faces the fence, it will give you a really nice detail and hide the fence a little bit. Also I would use aluminum pole and rings, so it last longer and sumbrella fabric which it is for outdoor. You can do a color fabric to brighten up the space, like yellow and blue or a neutral fabric like the picture above.

Painters tarps are often used and are very inexpensive. Below is a link regarding how to make and a hanging option or use grommets.

https://www.hometalk.com/1334760/how-to-use-painter-tarps-as-outdoor-drapes