When you are not beneath the waves (most likely when Friday morning comes along), there are plenty of other activities that you can do around the island. You can ask around for motorbikes to rent and you should be able to find one for IDR80k-100k for half a day. Most of the locals would recommend that you head to 'Kilometer Nol', the 'most northern point of Indonesia that is connected by road', about 15-20 minutes north of Iboih beach. I personally do not understand the attraction though as the only things you will find there is a very large and gaudy monument and a few stalls selling food and souvenirs scattered around. There is a small beach called Long Beach that is on the way to Kilometer Nol however that is quite nice, but if I had to recommend one place, it would have to be Gua Sarang.
Gua Sarang is a set of caves located along the the western coastline of Weh island. Looking down on the coastline is pretty breathtaking so be sure to take a moment to just sit down on the swing that you will find there in order to take in the magnificent views.
In order to get to the caves, you have to descend down a long flight of steps before turning left to cross a stony beach. The caves are famous for the edible nests of the brown-rumped swiftlet (Aerodramus vestitus), a bird that the locals call 'burung walet'. The nests themselves are made of the saliva of the swiftlets and are steamed in water to create soup that is said to have medicinal qualities. There is a narrow opening to get into the cave but the only thing of note inside the cave itself are the colonies of intermediate roundleaf bats (Hipposideros larvatus) that you can find perched upside-down on the ceiling.
If renting a motorbike to explore the surroundings doesn't sound appealing to you, Iboih beach is a lovely place to put your feet up and just unwind after a long, tiring day of diving.