As there is a problem leaving Eretz Yisrael except for work, for a shidduch, and so on, what are the connotations of just going there for a ‘holiday’ and then returning to live in chutz la’aretz?
For somebody who goes to Eretz Yisrael on holiday, there is no prohibition of leaving. According to some authorities there is a mitzvah of going to Eretz Yisrael, even for a short holiday, and there are other reasons for which Eretz Yisrael is a good choice for a holiday destination.
Sources: Several authorities discuss the question of whether or not there is a mitzvah of coming to Eretz Yisrael for only a temporary stay. Maharit (vol. 2, no. 25) writes that there is no mitzvah, but his proof (and opinion) is diputed by Chelkas Yaakov (vol. 1, no. 81). See also Shiltei Gibborim (Shevuos, chap. 3), and see also letters of Chazon Ish (vol. 2, no. 76). Mishnah Berurah (248:28) brings both opinions. From all of these sources, a clear assumption is that there is no prohibition of leaving Eretz Yisrael for somebody who enters with the intention of a temporary stay. The prohibition of leaving Eretz Yisrael applies only to somebody who lives there (and who can therefore be considered as “leaving”),
An additional reason for which Eretz Yisrael is a good choice for a holiday destination is that by going to Israel on holiday one fulfills the mitzvah of taking one’s custom to Jews, as ruled by Rema (responsa, no. 10), and quoted by later poskim. Additionally, one is able to infuse the holiday with spiritual content, such as visiting the kosel, kiveri tzaddikim, and so on.