One important thing to know is that Eilat is a small place, so it is definitely possible to walk almost everywhere, especially if you are staying at the north beach. However, you would probably need to take a taxi or use public transportation to get from the north beach to the south beach area.
In terms of public transportation, there is one company operating in the city – Egged. There aren't many urban bus lines but pretty much every line can take you close enough to where you need to go. Bus fare within the city is 4.90 shekels.
In addition, the short driving distances in Eilat (as we said it’s a small place) make it pretty cheap to travel by taxi in comparison to Tel Aviv, so you can indulge in an air-conditioned ride without thinking twice. Of course you can always choose to rent a car for your stay in one of the variety of car rental agencies operating in the city such as: Avis, Budget, Eldan, Shlomo SIXT and more.
New to Eilat is "Get Taxi" service which allows you to order a cab via the Get Taxi app and also has the possibility of payment with credit card.