Israel Gives is a directory and social giving platform (they take donations from around the world and donate to the organizations listed in their directory). you can use their advanced search features to get a list of organizations. You should then use Google to locate the organization's website for more research.
GuideStar collects information and shares on all non-profits registered with the IRS. GuideStar Israel lists each nonprofit organisation registered with the National Registrar of Non-profit Organizations in Israel.