If you can extend out the existing patio more and make it wider to possibly go past those windows, a pergola could be put along there. That would make a nice sized patio/entertaining area and an escape from the sun.

Adding a water fountain to your landscape design might be an idea. Check out photos for inspiration http://www.soothingcompany.com/water-fountains/outdoor-fountains.html

I agree with extending the patio I would suggest doing the patio out of pavers as it looks like you have a paver block wall. A landscape designer could help you with layout try finding on in your area through the find pros section.

Your backyard would be perfect for an outdoor living design depending on how much you will use the backyard. You can put a rectangle patio if it's a place you will not use much. If you enjoy the outdoors and love to entrain, it would be smart to get a design. You could have a fire pit or fire place area, a water feature, and a covered sitting area.

You have a terrific space and many options to turn it into just the right entertainment area. I agree with the others above, get an overall design from a landscape designer that you can implement as time and budget allow. Here are a couple of inspirations for you to get started on your dream backyard. If you start with a plan it will be much better for you. I don't know where you are, so these are random picks. You have more space in your back yard than many of us do :)