$("#btn_go").on('click', function(){
    if(validateUserDetails() == false){
            return;
    }
});

function validateUserDetails(){
    var bool = false;

    $.ajax({
        url: 'response.php?type=validateUserDetails',
        type: 'POST',
        dataType: 'json',
        data: {name: $("#checkout_name").val(), email: $("#checkout_email").val(), "country": $("#checkout_country").val(),
               "city": $("#checkout_city").val()},
        success: function(data){
            console.log(data); // this is currently returning FALSE
                               // Which is totally correct!
            if(data == true){ bool = true; }
            return trueOrFalse(bool);
        }
    });
}

function trueOrFalse(bool){
    return bool;
}

function validateUserDetails(){

return $.ajax({
    url: 'response.php?type=validateUserDetails',
    type: 'POST',
    async: false,
    dataType: 'json',
    data: {name: $("#checkout_name").val(), email: $("#checkout_email").val(), "country": $("#checkout_country").val(),
           "city": $("#checkout_city").val()},
    success: function(data){
        console.log(data); // this is currently returning FALSE
    }
});

$("#btn_go").on('click', function(){
    validateUserDetails().done(function(data){
         if(data == "someValue")
            return "whatever you want";
    }
});

function validateUserDetails(){

    // asynchronous function
    $.ajax({...});

    return undefined;
}

function validateUserDetails() {
    var bool = false;

    $.ajax({
            url: 'response.php?type=validateUserDetails',
            type: 'POST',
            async: false,
            dataType: 'json',
            data: {name: $("#checkout_name").val(), email: $("#checkout_email").val(), "country": $("#checkout_country").val(), "city": $("#checkout_city").val()},
            success: function(data) {
                console.log(data);  // this is currently returning FALSE
                                    // Which is totally correct!
                if (data == true) {
                    bool = true;
                }
            }
    });

    return trueOrFalse(bool);
}

function validateUserDetails() {
    var deferred = $.Deferred();
    var bool = false;

    $.ajax({
            url: 'response.php?type=validateUserDetails',
            type: 'POST',
            dataType: 'json',
            data: {name: $("#checkout_name").val(), email: $("#checkout_email").val(), "country": $("#checkout_country").val(), "city": $("#checkout_city").val()},
            success: function(data) {
                console.log(data);  // this is currently returning FALSE
                                    // Which is totally correct!
                if (data == true) {
                    bool = true;
                }
            }
            complete: function () {
                deferred.resolve(trueOrFalse(bool));
            }
    });

    return deferred.promise();
}

function test() {
    var promise = validateUserDetails();
    promise.done(function(result) {
        console.log("Bool: " + result);
    });
}