re: Back patio fireplace location thoughts

Where you have it looks like the best spot. Another possibility to look at is a built in fire pit. I was advised against a fire place, although they look nice I was told they don't give off much heat.

My area is uncovered so a fire pit works nicely. We can sit 6 and everyone can feel the heat.

Maybe a huge brick fire pit in the middle with a cupola roof in your covered area might be something to consider.