Issue: under this deck is poured concrete, about 12 inches above grade.

What material do you plan to use? Wood? Composite? I don't think a grille on either is very safe. Can you widen the deck to the AC unit? You need stairs off the deck, I would do them all the way across. Then a small patio for the grille.

This is mine. There's a brick patio for the grille

adding pavers at ground level could give you the extra space you need... how about a pergola over the patio door for some shade and interest?

I would extend deck for sitting area.

Or with pergola and side sitting area

With dining table on upper level?

I have wood deck in my outdoor kichen and also a smoker and grill and a stove with burners it is 16 yrs old and not ever been an issue for all the cooking we do outside. I do agree that the deck needs to be bigger and I like Celery's ideas . IMO the grill needs to be close to the kitchen and I usually think of outdoor entertaining the same as indoor the kitchen and dining space close together the seating more like the LR . Please do not do the red again anywhere except for maybe a pillow .