Aqaba is located next to the Israeli city of Eliat. It is possible to cross the border and visit this city from Aqaba. The two cities used to be one in the past.
Next to Israel is Egypt, which can also be visited from Aqaba, on a day-tour to Pharaoh Island, for instance.
South of Aqaba is Saudi Arabia (about 20 minutes by taxi). If you want to enter Saudi Arabia you will need a visa, though.
In the picture you can see the mountains of Israel from a beach in Aqaba.
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