Declaring variables inside or outside of a loop

The scope of local variables should always be the smallest possible.

In your example I presume str is not used outside of the while loop, otherwise you would not be asking the question, because declaring it inside the while loop would not be an option, since it would not compile.

So, since str is not used outside the loop, the smallest possible scope for str is within the while loop.

So, the answer is emphatically that str absolutely ought to be declared within the while loop. No ifs, no ands, no buts.

The only case where this rule might be violated is if for some reason it is of vital importance that every clock cycle must be squeezed out of the code, in which case you might want to consider instantiating something in an outer scope and reusing it instead of re-instantiating it on every iteration of an inner scope. However, this does not apply to your example, due to the immutability of strings in java: a new instance of str will always be created in the beginning of your loop and it will have to be thrown away at the end of it, so there is no possibility to optimize there.

EDIT: (injecting my comment below in the answer)

In any case, the right way to do things is to write all your code properly, establish a performance requirement for your product, measure your final product against this requirement, and if it does not satisfy it, then go optimize things. And what usually ends up happening is that you find ways to provide some nice and formal algorithmic optimizations in just a couple of places which make our program meet its performance requirements instead of having to go all over your entire code base and tweak and hack things in order to squeeze clock cycles here and there.

I compared the byte code of those two (similar) examples:

Let's look at 1. example:

package inside;

public class Test {
    public static void main(String[] args) {
        while(true){
            String str = String.valueOf(System.currentTimeMillis());
            System.out.println(str);
        }
    }
}

after javac Test.java, javap -c Test you'll get:

public class inside.Test extends java.lang.Object{
public inside.Test();
  Code:
   0:   aload_0
   1:   invokespecial   #1; //Method java/lang/Object."<init>":()V
   4:   return

public static void main(java.lang.String[]);
  Code:
   0:   invokestatic    #2; //Method java/lang/System.currentTimeMillis:()J
   3:   invokestatic    #3; //Method java/lang/String.valueOf:(J)Ljava/lang/String;
   6:   astore_1
   7:   getstatic       #4; //Field java/lang/System.out:Ljava/io/PrintStream;
   10:  aload_1
   11:  invokevirtual   #5; //Method java/io/PrintStream.println:(Ljava/lang/String;)V
   14:  goto    0

}

Let's look at 2. example:

package outside;

public class Test {
    public static void main(String[] args) {
        String str;
        while(true){
            str =  String.valueOf(System.currentTimeMillis());
            System.out.println(str);
        }
    }
}

after javac Test.java, javap -c Test you'll get:

public class outside.Test extends java.lang.Object{
public outside.Test();
  Code:
   0:   aload_0
   1:   invokespecial   #1; //Method java/lang/Object."<init>":()V
   4:   return

public static void main(java.lang.String[]);
  Code:
   0:   invokestatic    #2; //Method java/lang/System.currentTimeMillis:()J
   3:   invokestatic    #3; //Method java/lang/String.valueOf:(J)Ljava/lang/String;
   6:   astore_1
   7:   getstatic       #4; //Field java/lang/System.out:Ljava/io/PrintStream;
   10:  aload_1
   11:  invokevirtual   #5; //Method java/io/PrintStream.println:(Ljava/lang/String;)V
   14:  goto    0

}

The observations shows that there is no difference among those two examples. It's the result of JVM specifications...

But in the name of best coding practice it is recommended to declare the variable in the smallest possible scope (in this example it is inside the loop, as this is the only place where the variable is used).

if you want to use str outside looop also; declare it outside. otherwise, 2nd version is fine.

Declaring objects in the smallest scope improve readability.

Performance doesn't matter for today's compilers.(in this scenario)
From a maintenance perspective, 2nd option is better.
Declare and initialize variables in the same place, in the narrowest scope possible.

As Donald Ervin Knuth told:

"We should forget about small efficiencies, say about 97% of the time: premature optimization is the root of all evil"

i.e) situation where a programmer lets performance considerations affect the design of a piece of code. This can result in a design that is not as clean as it could have been or code that is incorrect, because the code is complicated by the optimization and the programmer is distracted by optimizing.