How do I give this space an awesome make-over?

A path to the door would be lovely, as well as trellises along the walls to grow plants vertically, possibly in raised beds. It looks like containers may be the way to go based on the ground you're working with, but gravel or rocks between the containers would also look great.

https://www.bhg.com/gardening/plans/

I had an area just like that in a house I used to own and I put in rose bushes of varying colors. I also used trellises.

This space has so much potential! I love the brick walls, I would add a pretty outdoor rug and make a little sitting area. Soften up the brick walls with tall potted plants or arborvitaes!

It needs color lots of color, do you want a sitting area??? trellises are a good idea, you could also add small planters on the wall, also put in a water feature (like a fountain or rain wall. also needs a place to sit either a chaise lounge or an Adirondack chair with a side table to put a glass of tea or a good book , a path from the gate to the door using flagstone or gravel or stepping stones over to the sitting area also

You could carefully deconstruct the BBQ structure and use the bricks to make raised flower bed across the long wall with a wall mounted fountain above a small pool. You could put up trellises on either side of the fountain. Then buy wrought iron plant stands and group them around the area. Some lanterns on the patio as well as hanging lanterns would be great. Just add furniture. If budget allowed a pergola over the area would be nice. I like the tile, I would find some other tile that is the same color and add to the patio. I don't know what your climate is like, but it looks like Arizona or Southern California. If so, bougainvillia would look nice planted for the trellises.

..in a sense, all of the above Plus there are wonderful paints that work on brick. Imagine just white, then the trellises..etc..I’m very big on climbing roses..Japanese art does amazing things with perspective..illusions of great distance..Yours is a wonderful opportunity. Great luck.

Thanks for all the great ideas. I am going to do a path to the gate, trellises, stone and either containers or raised flower beds. And definitely a sitting area. Hopefully I can share the transformation soon.