If someone lives in Eretz Yisroel, may he travel to Eilat for a vacation? The first issue that must be addressed is, is Eilat part of Eretz Yisroel? Rav Shmuel HaLevi Vosner in the Shevet HaLevi (5:173) says that almost certainly without a doubt, Eilat is not part of Eretz Yisroel.
This brings us to the issue of leaving Eretz Yisroel. The Rambam in Hilchos Milachim (5:9) paskens that it is forbidden to leave Eretz Yisroel to go to Chutz La’Aretz. Regarding this, says the Shevet HaLevi, it is clear from the Rambam that the main prohibition is going to Chutz LaAretz to take up residence there. The only time this is permitted is if there is a severe famine in Eretz Yisroel. For someone leaving on a temporary basis, whose place of residence is still established in Eretz Yisroel, it is permissible to leave if there is a “Tzorech”, a need. This includes traveling for business even if you are not lacking sustenance.
Leaving for no Tzorech whatsoever is not permitted according to Rav Vosner, and this he says would logically include a pleasure trip. Nevertheless, he says that if someone were to travel for a very short time with the purpose of enjoying the natural marvels of our Holy Creator’s world, in that case if he has in mind that he wants to do a mitzva, there is room for leniency.