I like our 2" thick 12x12 pavers edged in orange brick laid on a sand base. It was a lot more work than we 1st thought because our ground wasn't level. I wish we would have checked that before we started excavating the soil.

If you're going to DIY instructions are available online for building a base. I highly recommend you follow the advice so that your patio has the correct slope for drainage & stays in place. It's hard work digging, leveling, tamping, carrying & spreading sand, moving pavers, etc. & you don't want to have to do it over.

An evergreen climber on a trellis would screen views. If you want partial shade you might consider a pergola and grow grapes or other edibles on it.

You mentioned a child & I've found that our younger visitors enjoy playing on the lawn, wood chip area under the cedar tree, or the wooden deck rather than the paver patio. You might consider a more forgiving surface while your child is young. I'm also more relaxed when our nephew is on the lawn or deck with resin furniture than on the patio near the iron furniture.

When our kids were young we had a covered sand box that was enjoyed nearly year round then when they were done with it the sand went into the garden & we gave away the sand box. We kept the sand toys & trucks right in the sand box underneath the lid, so it was easy to remove the lid & play.

In my area the cedar play chips are readily available & make a nice covering that stays dry during wet winters. Unplanted areas where our lawn wouldn't grow because of shade or where we walk a lot to the hose and to the chicken coops have been covered with the play chips and cedar arborist chips. I like the weathered look that is easy to maintain because it never need mowing, watering, or weeding! On occasion rake a bit & renew to keep the depth.

If you think you might want to grow plants at some point in your backyard you may want to use chips now & let them decompose then when your child is older you could rake them aside & layer compost materials for growing vegetables & fruits.

Hope that helps!

Ditch those palms. Soon they'll be fruiting and dropping rotting stinking slimy orange fly-attracting fruit all over your tiny yard. They'll need frond-trimming and it ain't cheap.

Since your yard is so very, very small, anywhere you need privacy screening, put up a sturdy trellis as tall as you can lawfully get away with and grow more of that Star Jasmine on them. You will get very effective privacy screens that way with a minimum of space used. If you need shade, get a patio umbrella and if you like palms put a Sago in a pot.

If I were designing the space for myself I would use flagstone for the patio, but I wouldn't want it to take up the entire courtyard. I would build a semi-circular patio with a flat edge against the house and curved sides bordered by a soft groundcover like thyme. I would either install lattice or espalier plants against the walls to give a softer and greener look. Lastly I would turn the drain into a positive feature by using natural stone to make it look like a dry creek, if possible I would plant some drought tolerant natives among the rocks. I think it would look wonderful to have a vine-draped trellis with a bench or swing underneath against one of your walls, but if you don't have room an umbrella would be a good alternative.

I always like to use graph paper to draw up a few different variations of a plan and then show them to people to ask for opinions. You can never see everything from one perspective so asking other people for advice is very helpful.

Good luck!

After looking more closely at your pictures I have to change my advice a little, I don't think a dry stream will work with that drain. But since it's not good to put a trellis directly against a wall, a 6-12 inch gap is recommended, it might be best to install trellises along the drain to hide it from sight that way.

If you have any interest in edible landscaping there are columnar apple trees that are suitable for growing in containers, you can find some good examples by doing an image search for 'potted columnar apple.' I have never grown one myself so I cannot say how well it will do as a screen for a bad view. Your best bet on finding a really good potted screen plant will probably be going to a local nursery and asking for advice there. Also if you decide to have an arbor with grape vines on it I highly recommend choosing an American grape (like Concord) instead of a European (like Thomson seedless) because of their better disease resistance.

Did you just plant the palms, or have they already been removed? I hope they have been removed, but if not, you should get rid of them fast before they ruin your life and your patio.
Queen palms are a terrible plant. The roots will invade your drain and block it. The trees begin fruiting at a young age and the date bunches weigh 75- 100 pounds. Thousands of messy, orange dates all over your patio all year round. The pointy-ended sheaths that encase the date bunches burst open and dry, and fall down with enough force to skewer a large person. It cost me over 700 bucks a year to have three of them pruned. The flower litter alone was enough to ruin the pond and clog the pump. You can't plant anything under them, because the orange roots are so tough and so dense that there is no soil left for anything else to grow in. I finally had three of them removed when I found palm roots growing between my concrete slab and the tile in my bathroom. They had gotten into my clay sewer pipes too.

They are pretty, though, aren't they?
Renee

lol....Pretty...lol. and I see acre after acre of Queen Palms being grown for the poor unsuspecting people who buy and plant them....lol. They should come with a warning label..