Here I have created sample that will help you out.

You need to set async to false.Please refer below article

jQuery AJAX: Async False (Synchronous call) and Async True (Asynchronous call) difference

HTML

<div>
    <script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.7.2/jquery.min.js"></script>
    <script type="text/javascript">
        $(function () {
            LoadCity();
            LoadLocalCity();
        });
        function LoadCity() {
            $.ajax({
                type: "POST",
                url: "Default.aspx/GetCategory",
                data: '{}',
                contentType: "application/json; charset=utf-8",
                dataType: "json",
                async: false,
                success: OnSuccess,
                failure: function (response) {
                    alert(response.d);
                },
                error: function (response) {
                    alert(response.d);
                }
            });
            function OnSuccess(r) {
                var categorys = r.d;
                var repeatColumns = parseInt("<%=chkItems.RepeatColumns%>");
                if (repeatColumns == 0) {
                    repeatColumns = 1;
                }
                var cell = $("[id*=chkItems] td").eq(0).clone(true);
                $("[id*=chkItems] tr").remove();
                $.each(categorys, function (i) {
                    var row;
                    if (i % repeatColumns == 0) {
                        row = $("<tr />");
                        $("[id*=chkItems] tbody").append(row);
                    } else {
                        row = $("[id*=chkItems] tr:last-child");
                    }
                    var checkbox = $("input[type=checkbox]", cell);

                    //Set Unique Id to each CheckBox.
                    checkbox[0].id = checkbox[0].id.replace("0", i);

                    //Give common name to each CheckBox.
                    checkbox[0].name = "CityId";

                    //Set the CheckBox value.
                    checkbox.val(this.Value);

                    var label = cell.find("label");
                    if (label.length == 0) {
                        label = $("<label />");
                    }

                    //Set the 'for' attribute of Label.
                    label.attr("for", checkbox[0].id);

                    //Set the text in Label.
                    label.html(this.Text);

                    //Append the Label to the cell.
                    cell.append(label);

                    //Append the cell to the Table Row.
                    row.append(cell);
                    cell = $("[id*=chkItems] td").eq(0).clone(true);
                });

                $("[id*=chkItems] input[type=checkbox]").click(function () {
                    var cell = $(this).parent();
                    var hidden = cell.find("input[type=hidden]");
                    var label = cell.find("label");
                    if ($(this).is(":checked")) {
                        //Add Hidden field if not present.
                        if (hidden.length == 0) {
                            hidden = $("<input type = 'hidden' />");
                            cell.append(hidden);
                        }
                        hidden[0].name = "CityName";

                        //Set the Hidden Field value.
                        hidden.val(label.text());
                        cell.append(hidden);
                    } else {
                        cell.remove(hidden);
                    }
                });
            };
        }

        function LoadLocalCity() {
            $.ajax({
                type: "POST",
                url: "Default.aspx/GetCitylocation",
                data: '{}',
                async: false,
                contentType: "application/json; charset=utf-8",
                dataType: "json",
                success: OnSuccess,
                failure: function (response) {
                    alert(response.d);
                },
                error: function (response) {
                    alert(response.d);
                }
            });
            function OnSuccess(r) {
                var locations = r.d;
                var repeatColumns = parseInt("<%=Chklocal.RepeatColumns%>");
                if (repeatColumns == 0) {
                    repeatColumns = 1;
                }
                var cell = $("[id*=Chklocal] td").eq(0).clone(true);
                $("[id*=Chklocal] tr").remove();
                $.each(locations, function (i) {
                    var row;
                    if (i % repeatColumns == 0) {
                        row = $("<tr />");
                        $("[id*=Chklocal] tbody").append(row);
                    } else {
                        row = $("[id*=Chklocal] tr:last-child");
                    }

                    var checkbox = $("input[type=checkbox]", cell);

                    //Set Unique Id to each CheckBox.
                    checkbox[0].id = checkbox[0].id.replace("0", i);

                    //Give common name to each CheckBox.
                    checkbox[0].name = "localid";

                    //Set the CheckBox value.
                    checkbox.val(this.Value);

                    var label = cell.find("label");
                    if (label.length == 0) {
                        label = $("<label />");
                    }

                    //Set the 'for' attribute of Label.
                    label.attr("for", checkbox[0].id);

                    //Set the text in Label.
                    label.html(this.Text);

                    //Append the Label to the cell.
                    cell.append(label);

                    //Append the cell to the Table Row.
                    row.append(cell);
                    cell = $("[id*=Chklocal] td").eq(0).clone(true);
                });

                $("[id*=Chklocal] input[type=checkbox]").click(function () {
                    var cell = $(this).parent();
                    var hidden = cell.find("input[type=hidden]");
                    var label = cell.find("label");
                    if ($(this).is(":checked")) {
                        //Add Hidden field if not present.
                        if (hidden.length == 0) {
                            hidden = $("<input type = 'hidden' />");
                            cell.append(hidden);
                        }
                        hidden[0].name = "localcity";

                        //Set the Hidden Field value.
                        hidden.val(label.text());
                        cell.append(hidden);
                    } else {
                        cell.remove(hidden);
                    }
                });
            };
        }
    </script>
    <asp:CheckBoxList ID="chkItems" runat="server" RepeatColumns="1">
        <asp:ListItem Text="" Value=""></asp:ListItem>
    </asp:CheckBoxList>
    <br />
    <asp:CheckBoxList ID="Chklocal" runat="server" RepeatColumns="1">
        <asp:ListItem Text="" Value=""></asp:ListItem>
    </asp:CheckBoxList>
</div>

C#

[WebMethod]
public static List<ListItem> GetCategory()
{
    DataTable dt = new DataTable();
    dt.Columns.Add("CityId");
    dt.Columns.Add("CityName");
    dt.Rows.Add(1, "Mumbai");
    dt.Rows.Add(2, "Thane");
    List<ListItem> categorys = new List<ListItem>();
    foreach (DataRow dr in dt.Rows)
    {
        categorys.Add(new ListItem
        {
            Text = dr["CityName"].ToString(),
            Value = dr["CityId"].ToString()
        });
    }
    return categorys;
}

[WebMethod]
public static List<ListItem> GetCitylocation()
{
    List<ListItem> locations = new List<ListItem>();
    DataTable dt = new DataTable();
    dt.Columns.Add("localid");
    dt.Columns.Add("localcity");
    dt.Rows.Add(1, "Sub-Mumbai");
    dt.Rows.Add(2, "Sub-Thane");
    foreach (DataRow dr in dt.Rows)
    {
        locations.Add(new ListItem
        {
            Text = dr["localcity"].ToString(),
            Value = dr["localid"].ToString()
        });
    }
    return locations;
}

Screenshot