Six of Shinou's GYMs can be made out from this scan. One is in the lower left, in the town with a canal running through its middle. Another is in the town against the mountains, the 'mining' town. Another is across the bridge (?), north of the 'mining' town. There is another on the right most side of the map, in the town above the lake. Another is in the town below the lake. And the last one that can be made out is in the town with the Contest Dome, on the mountain's right side. Or on the other side of the 'mining' town if that makes things easier.
So that leaves the locations of two GYMs still unknown. Though I'm guessing one of them is in the north most side of Shinou, in the snow covered town. And the last perhaps on the island that this map doesn't show.
Is it just me, or do the locations of the GYMs, seem more spread out this time around? With the first GYM being found in the 'mining' town, I'd imagine the last to be one of the two that we still don't have locations for. I can see the second being either the one across the bridge (?), north of the 'mining' town, or in the town with the canal running through on the far left. With the other being the third GYM of the game.