And a link to my ideabook of things I like: http://www.houzz.co.uk/ideabooks/53886065/thumbs/living-room

I love wooden shelving although it does involve quite a bit of dusting! Etsy have lots of carpenters selling shelves, some made of scaffold boards. A sideboard could be a good option if you need more storage. A large piece of art would also be good maybe against a darker painted wall? Sometimes less is more.

Adding some greenery to the empty corner could indeed help soften the expanse of tile and stone, creating a more inviting and balanced outdoor space. You might also consider some permanent fixtures like a small statue or a wind-resistant shrub that ties in with the existing Myrtus planter if you don't want to opt for a larger, heavier pot. For the area on the right at the top, since it also appears quite bare and has an olive tree nearby, perhaps a couple of matching pots or as Isla said, a bench or some seating could unify the space and provide both aesthetic appeal and functional seating.

Since you can move the fireplace first decide on a function for the room. A lounge end with a fireplace is a good feature to have, Think about the furniture that will be there as well as flooring and window treatments. It all needs to work together. Fireplaces come in so many styles now you can match it to whatever you desire. I would be tempted to move it close to the bay window end and have that as a lounge area, keeping the other end for the tv and a possible media wall.