I currently attend a Chabad shul and I don’t like the way the prayers are led in the Ashkenazi accent, what other religious groups are there in Israel that I may enjoy the prayers? Are there other Chassidic movements besides Chabad?

There are many Chassidim in Israel who are not Chabad - Ger and Belz and Sanz to mention just three. Most Chasidim daven in an Ashkenazi accent. There are- thank G-d- Orthodox shuls of of every kind throughout the country. Find one where you feel comfortable.