El Al and Royal Jordanian Airlines both fly to Amman, Jordan's capital, from Tel Aviv's Ben Gurion Airport. This option has limited appeal, as you must be at the airport two hours before flight time for the 15-minute flight, then drive three hours from Amman to Petra.
Many people use Eilat, the resort city at the southern tip of Israel, as a base for exploring Petra. There are frequent flights to Eilat from Tel Aviv and Haifa. Two domestic airlines serve Eilat: Arkia and Israir. A new international airport is under construction there and expected to open sometime in 2017.