There is a trail that runs right around the island but, as on Gili Trawangan, it gets thick with sand in places.
There is also a network of (mostly sealed) roads in the interior that make it very easy to explore the island. There are plenty of coconut plantations to ride by along with a few villages where life goes on oblivious to the developing tourist scene that surrounds them.
Bikes can be rented for 30,000 rupiah a day — if grabbing for a longer period ask for a discount.
While Gili Air is bigger than Meno, it is a good deal smaller than Trawangan, meaning it can be easily walked around if you don't want to grab a bike. Walking at a steady pace, a round-island walk should take a couple of hours, though if you pack a hat and some snorkelling gear you could spend the day walking around and fit some snorkelling in.