I don't see the "flat part at the bottom" where you want to plant grass ... so can't comment. Would not plant any grass above the retaining wall. It is better suited to groundcover. Would get rid of all grass and weeds there (but not trees and shrubs) and plant a nice, low groundcover.

On the patio put some nice furniture ... table, chairs umbrella and a few large planters with something colorful in them. There could be a window box, too.

Don't try planting anything in a dog trail.

Thanks... :-) I see that it is hard to see the flat part in the pictures. Below is a picture that shows it better. The reason I spoke about grass is that I want to be able to walk about on the flat part and not have to weed whack it when the weeds get high. A low groundcover would be bad in case the dog goes here, and we wouldn't be able to see it and step in it!! There is some groundcover around on the slopes, some ivy, some barren strawberry (I think), maybe some others. I was thinking about planting some azaleas along the bottom of the slope; there is already one there to the left just out of the picture. Or maybe some along the top of the wall. Maybe clematis to fall down over the wall...

How will you mow up there?

I can take the mower either up the steps, or push it up on the other side.

You sound young and strong. Or at least strong. I thought you might mean that area. That is why I made the dog trail remark. Ivy and strawberry are both aggressive. You will have a hard time keeping them out of the grass. If you can handle the work then plant the lawn.

I'm not young but I'm strong... :-) Yes, that is a concern. If we just leave it natural, as it is, there's not a lot of work. But that's no fun. However, it will be hard just putting grass there (would need topsoil). I will have to think long and hard this winter.

what's the difference between weed whacking and mowing? You still have to get up there and operate a machine. Is there another surface that would be suitable in that narrow strip for your dog? Maybe a brick border with crushed gravel?

My experience with dogs is that they are happy to have trails through the space, to give them places to sniff, explore, and run around. I'd put a mulch path up there at the base of the sloped part, and low ground cover on the flat part between the path and the wall on the house side of the space. (You can then easily walk the path, looking for any 'doggie land mines' that need picking up in the groundcover.). That should look good and be less work for you; the dog would be happy too.