Multisite: Redirect Subsite Administrator to Subsite Home Page, Bypassing Dashboard

You can use the login_redirect filter:

add_filter( 'login_redirect', 'wpse_159078_login_redirect' );
function wpse_159078_login_redirect( $redirect ) {
    if( ! current_user_can( 'update_core' ) ) {
        // if it's not a super admin that's logging in
        $redirect = get_home_url();
    }
    return $redirect;

}

References

• login_redirect filter
• get_home_url()