I think I'd start with a hedge to hide the fence. I'd do a plant around the entire perimeter of the fence that includes some small ornamental trees and shrubs which, in a short time, will also cover the view of the neighbor's homes. Go to your local garden center store and consult with them to draw up a plan for what will grow the best in your area and enhance your home. It's an important investment and rewarding to enjoy. They can do the planting and work with your budget.

Haha you do NOT want to see my backyard. We're getting ready to rip out a huge nasty old pool and totally redo the entire yard. Good luck with yours! :)

"Show me your back yard" seems like it would be somewhere between hi-or-miss or the-long-way-around, if the goal is getting something for this back yard. It's kind of like saying here is a naked body .... what outfits would work? Well, only a million different outfits! Instead, it would be good to work through the normal design process, beginning with inventory and assessment of what's there (which does not show in the two photos), and then analysis ... to concept and narrowing of the possibilities into a cohesive plan in which some practical, applicable solutions would emerge.