Where are you in your own home or on your property when you see this view? Can you take another pic to give us more context to work with?

Add 3 or 5 more evergreen trees like the ones you have now or maybe American holly. Place them with some forward and some back--don't do a straight line.

Keep the tops trimmed so they get bushier and don't grow tall and slender.

That's pretty much an instant fix for a thoughtless neighbor. A fence could also work but might be more expensive than a few trees.

You may have to lose the two smaller crisscrossed trees in the center of the photo. Then plant one or more evergreens, one where the small tree on the right is... You also may have to thin out or remove the larger tree on the right to give the evergreens enough light to flourish and grow fast as possible. Be sure and protect the new trees from animal damage to keep the lowest branches from dying.

This picture is taken from our backyard patio which we are in the process of finishing with bluestone.

A wall of carefully-chosen lattice installed on the outside of the perimeter of your new patio could do the trick. While most of the lattice I've seen comes in an X orientation, it seems that a checkerboard arrangement looks more elegant. Make it just tall enough and long enough to hide the ugly view. I have a similar (worse, actually) situation--the view into my neighbor's tragic backyard from my covered deck is nightmarish--but I was able to hang outdoor curtains and my problem was solved. Is it likely that anyone will want to venture out from the patio into the grass area? They'll simply go to the other side of the lattice. If not, you'll almost forget that all that unsightliness is there. Good luck!

Natural screens. There are many fast growing evergreens that would work as a screen. Perhaps bamboo, there are varieties that don't spread.