If you are going to leave the tall hedge, I would personally leave the tiles and change the feel instead with lots of potted trees and plants. You essentially have a lovely outdoor room, not a yard. Maybe swap out the large picnic table for a more intimate garden bistro set with chairs and/or a loveseat with cushions/pillows? A small outdoor rug? Surrounded by potted plants of various heights that you can arrange and layer continuously as desired, this can become a beautiful little garden haven that is both cozy and comforting while easy to maintain.
No telling what quality the ground is under those tiles, and I would imagine that the hedge is going to impact growth ability of whatever you plant in their place.
Big Cheese, man, nothing to mess with.