There are a few schools in Israel that offer Arabic studies, among them: The Hebrew University and The Center for Jerusalem Studies.
Each of the schools I've mentioned above offers a different program but in general they focus on Palestinian Arabic and Modern Standard Arabic.
I've attached a link at the end of my message to an article about the different courses you can choose from and offer information about each institute in Jerusalem and outside of it so you could compare the institutes in Jerusalem to the other institutes in Israel.