There appear to be 2 treasures marked with X on the map. One is at (15°S, 120°W); the other is at (45°S, 120°E). The first of these is both northernmost and westernmost. The second of these is on its own island. Since it is the only treasure that is not the northernmost, it is also the closest to the northernmost.
- (15°S, 120°W)
- (15°S, 120°W)
- (45°S, 120°E)
- (45°S, 120°E)
_____
Comment on the map
There appear to be additional features marked with a double "circle". We cannot tell if these are mountains, or are supposed to represent treasure locations. They are generally at spots that would require interpolation of the coordinates, so we suspect they are not relevant to the problem. Both "land masses" are completely surrounded by "water", so we aren't sure which is to be considered "its own island". A legend could be helpful.