June can be sometimes even better than April or May, because the latter are transfer months with fast changing weather. Anyway, it's on you luck. Sometimes in April you can have 40 degrees for a week - but very rare. In June the weather is more stable and usually nice.

Eilat is not only a beach resort, but the place with the Northern-most coral reef, great red mountains landscape with amazing Timna Park, interesting Aquarium and an option to take an organized day trip to Jordan's Petra. A real must. Try to not miss it. It will be an unforgettable experience.

Getting to Eilat can be nice through the Dead Sea with a night-two stop to relax there and to have interesting trekkings or jeep travels in the Judea desert. It's another gem!

Coming back from Eilat you can pass through the Machtesh Ramon gorge. Also, my strong recommendation.

Welcome to Israel and have a nice trip, Alex Elbert Jerusalem Israel