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If you can put doors on the whole back area and deck or pave out to a functional size for entertaining - be sure to have as close to same height as inside and the whole width of the house if possible. You could do the pergola which looks gorgeous and makes a cozy feel. On top of the pergola you may be able to do a weatherproof retractable awning if you do not want a permanent covered area. That would make a whole area for indoor outdoor entertaining in all types of weather. You can still have a step down area to grass and plants at the rear. Travetine is great and easy to hose down. You do not have to concrete them down use pavers on a good road base. You would have to speak to the experts about how to get the right height - also be sure to have a slight fall away from the house.

Looks like the drain that the down pipe goes into isn't working as it should, over flows before water enters the drain. Love the random pavers, these could certainly be reused adding a few more to replace the bricked area all on one level as this would enable a better space for outdoor table and chairs. The pergola is tired and would be great if as you mentioned could be raised up a bit, depends on what the Body Corporate will allow, a couple of see through panels inserted above next to the building would help with light. A BBQ kitchen on the back wall, plus I would try to re swing the door back to it, the door gets in the way as it is, can it open inwards opposite the sink. Certainly keep the garden beds it will help soften all the hard surfaces, taller planting along the boundary will also add privacy cheers

Looks fabulous.