C++ where to initialize static const

Since C++17 the inline specifier also applies to variables. You can now define static member variables in the class definition:

#include <string>

class foo {
public:
   foo();
   foo( int );
private:
   inline static const std::string s { "foo" };
};

In a translation unit within the same namespace, usually at the top:

// foo.h
struct foo
{
    static const std::string s;
};

// foo.cpp
const std::string foo::s = "thingadongdong"; // this is where it lives

// bar.h
namespace baz
{
    struct bar
    {
        static const float f;
    };
}

// bar.cpp
namespace baz
{
    const float bar::f = 3.1415926535;
}

Anywhere in one compilation unit (usually a .cpp file) would do:

foo.h

class foo {
    static const string s; // Can never be initialized here.
    static const char* cs; // Same with C strings.

    static const int i = 3; // Integral types can be initialized here (*)...
    static const int j; //     ... OR in cpp.
};

foo.cpp

#include "foo.h"
const string foo::s = "foo string";
const char* foo::cs = "foo C string";
// No definition for i. (*)
const int foo::j = 4;

(*) According to the standards you must define i outside of the class definition (like j is) if it is used in code other than just integral constant expressions. See David's comment below for details.

Static members need to be initialized in a .cpp translation unit at file scope or in the appropriate namespace:

const string foo::s( "my foo");