San Andrés' airport is in San Andrés Town, a 10-minute walk from the town center, or an expensive COP$15,000/7000 ride by taxi/moto-taxi. If you don't have much luggage, it's an easy walk: turn left out of the terminal building, then turn right onto the main road, which will become Av Colombia. There's a left luggage room at the airport (COP$4000 per item per 24 hours).
The best way to travel independently around the island is by scooter (from COP$60,000 per day) or golf buggy (from COP$100,000 per day). Many of the rental businesses are on Av Newball in San Andrés Town and are concentrated around the tip of the island. Most will also deliver to your hotel. Shop around as prices and conditions vary. One place we recommend is Rent A Car Esmeralda.