The neighbor’s home will feel a lot less prominent when you have other focal points in the yard — planting beds, trees, fire pit, seating area, grill station etc.

Have the neighbors moved in yet? Sneak over and plant some stuff on their side! :)

But really, I don't understand why there's no width on your side. It looks entirely empty. Which spot exactly?

With the ongoing water crisis in the SW, I suggest looking into native trees. You might have to use shade sails and other interesting architectural elements instead of relying solely on plants.

I think Fori is right about plenty of space. You may be thinking the plants have to follow the fence line in order to avoid blocking the view of your yard from the patio. If you plant trees, though, most of what you will see in your sight line will be the trunks, while all the foliage will help to hide your neighbors house, rather than the fence. Also, trees planted further away from the fence line will offer you privacy from your rear neighbors.

Actually, the trees your rear neighbor has planted look like they might work for you, too. I think all that repetition will make the landscaping look more natural, particularly if they are spaced somewhat randomly, rather than in a row.

Thanks for the comments for far! The green poles I drew in the pic was what I was thinking - like Italian Cypress trees or something but even those I think would get too thick. And yes tree trunks would be useless.

I have no idea why the developer decided the backyard access side of the house should be close to the fence while there is copious space on the other (dead) side - DOH!

We'll worry about the rest of the landscaping later but this part is the worst as the neighbors see right in your house. There are NO back neighbors - its protected land and mountain views so we wouldn't want to block that with trees!

Perhaps you can get creative with sail shades that extend from the top of the fence to your patio roof. More shade would be nice!

Here’s a photo illustrating your idea too simply add more height to the fence.

"simply add more height to the fence."

I did this years ago at one house though the boards were vertical. It does work for lack of anything else then landscape as normal and maybe add some decoration to the wall itself.