We took a ferry from Padang Bay directly to Gili Air. We heard from several people that it was a nice island with a few interesting features: very small size and no motorized vehicles.
Indeed, the island is about 1km in diameter and we've seen zero fuel-powered vehicles, although horse-drawn carriages are allowed, and a lucky few have electric motorbikes.
The island has a very relaxed atmosphere. It only took a couple hours' walking around and overhearing music at several bars before we nicknamed Gili Air after its official soundtrack: Jack Johnson Island.
We found a really great place to stay called Goodtimes Bungalows. It's run by a Norwegian family and they are some of the friendliest, most generous hosts we've met on our whole trip.
They built a great property and have done it according to all the customs of the locals, which not all businesses do. They are very eco-friendly, with the hot water coming from a solar panel, and they plan to eventually power the entire property by solar+batteries.
They also serve delicious breakfast at a great price, and are always helpful when we had questions about the island, or even lent us a bit of equipment to go snorkeling. We're so happy to have stayed here. Good times!