The village itself is easily walkable along the seafront road, and the Glenashdale Falls trailhead is within easy reach on foot from anywhere in Whiting Bay. The path up to the Giants' Graves starts from the village as well.
To explore the rest of the island, a car is the most flexible option. The circular island road is 56 miles and easily driven in a day, taking in the varied scenery of both coasts. Cycling is also rewarding — bike hire is available in Brodick — though the road has some hills. The local bus makes a circuit of the island but runs infrequently, so time your connections carefully.