Method public static org.openqa.selenium.WebDriver MyTestNG.Baseurl.basic() Error

Question

In Baseurl.java, driver is not declared as a global variable. It is declared under basic(). This means driver is accessible only under basic().closeBrowser() cannot have access to driver, hence you are getting the error.

I have a few suggestions to your code.

I believe Baseurl.java is not the class under test. It is provided merely to start and close the browser. So remove the annotation @Test from it.
Countrychoser.java is your test class. So add @Test to it before the method Choser(). I also suggest you make the Choser() method non static.
I see that you have used finally block to close the browser. Since you are using the TestNG framework, you can explore the possibilities of @AfterTest annotation instead.
Similarly @BeforeTest annotation is also useful.

To sum it up, please have at a look at your code with the modifications :-

Baseurl.java

public class Baseurl {
    private WebDriver driver; //global variable

    public static WebDriver basic() {
        driver = new FirefoxDriver();
        driver.manage().deleteAllCookies();
        driver.get("http://www.sears.com/shc/s/CountryChooserView?storeId=10153&catalogId=12605");
       return driver;
    }

    public static void Closebrowser(){
        driver.quit();   //  You wont get an error now :)
    } 
}

Countrychoser.java

public class Countrychoser {
    WebDriver driver;

    @BeforeTest
    public void startTest(){
        driver = Baseurl.basic();
    } 

    @Test
    public void Choser() {
        try {
            //driver.findElement(By.className("box_countryChooser")).click();
            driver.findElement(By.id("intselect")).sendKeys("India");
            driver.findElement(By.xpath(".//*[@id='countryChooser']/a/img")).click();
            //window.onbeforeunload = null;
            System.out.println("---------------------------------------");
            System.out.println("Country choser layer test case-Success");
            System.out.println("---------------------------------------");
        } catch(Exception e) {
            // Screenshot.pageScreenshot();
            System.out.println(e);
            System.out.println("---------------------------------------");
            System.out.println("Country choser layer test case Failed");
            System.out.println("---------------------------------------");
        }
    }

    @AfterTest
    public void endTest() {  
        // Screenshot.pageScreenshot(); 
        // Baseurl.Closebrowser();
    }
}

Let me know if this helps you.