In order to use Grapple Hook Ropes, you need the Pirate Costume. For information on how to obtain the costume, see here.
1 - The first grapple hook location is just before the first bridge that you can cross over, you need to head southwards from said bridge, walk off what seems to be a waterfall and follow the wooden planks down till you get to it.
2 - The second is just northwards, but in the same area, as to where you find the chest that has the Eyepatch material in.
3 - Third grapple is found at the top of the scaffolding type area, next to the monster gate in the east of the town.
4 - This one is a required grapple, you need to gain entrance to a tomb for the Trowbog elder.
5 - Another mandatory grapple, you need to be on the way to find the yeti, through the first cave.
Extra Grapple Locations
6 - After getting to the snowy ledge, before heading into the yeti cave, you can head east, up some wooden planks. It heads back down to the gate.
7 - Mandatory grapple point, you need to do this to carry on the game. It is located up the slope after opening the final gate.