Lets start with the fireplace. Even if you could run wires to it it's way to high. Not only would it be uncomfortable to watch you would be giving up some picture quality because of the off axis viewing angle.
It's a beautiful room with lots of light, but that presents a lot of problems with layout options. You can't use any of the side wall because of the doors and whatever furniture layout you end up going with.
It really comes down to the four corners. You only have two of the corners pictured so it's hard to give you an exact answer.
If you went with the far corners by the doors I actually think the best spot is where the TV is located now. I wouldn't see the need to remotely locate the equipment unless you have a lot of sources (if it went in one of those two far corners) It's a waste of money. Put the money into a nicer cabinet, TV, speakers, or a universal remote. And yes you would have to block one of those two doors, but it looks like you have plenty of other doors to get outside
Plus sometimes you have to make compromises based on the layout of the room.
The room is also not conducive for surround sound either. I would either do a soundbar/sub combination or a stereo/sub combination with a receiver (use a surround receiver with video switching if you have a few sources or want to simply using the system). Put the TV on top of a corner cabinet, put the components inside the cabinet, and pick out a cabinet with a built in spot for a soundbar or a pair of small bookshelf speakers that you could also locate in the cabinet.
Example of cabinets...
(they have different finishes)
or this... (if you are on a budget and don't mind seeing wiring)
When picking out furniture you need to take in account the size of the TV, the style of cabinet you are looking for, the width of that corner, the amount of equipment you have, and your budget when considering the furniture. You could place the sub behind the cabinet, in a corner, or behind a piece of furniture.
If you put the TV in the other un-pictured corners you could probably mount the TV on the wall and put the gear in the cabinet in the adjacent room. Just keep in mind that you need to get power to the TV and equipment location, as well as a cable line and possibly internet at the equipment location. Those two corners would also have a lot of light shining on them (doors and windows instead of just doors) so the TV might be harder to view. You should check to see what kind of light you get in that room during the day before making a decision. With this set up I would either do a soundbar/sub combo or a pair of in-wall or on-wall speakers depending on the look you were going for.
And yes I am a professional and do this stuff for a living. So I have a lot of experience with difficult rooms.
Hope this helps.