Originally Posted by joejones

If you're going to do that, it may be faster and just as cheap to take the Keisei Skyliner or limited express (whichever is departing first) to Nippori, then change to the southbound Yamanote Line, which also goes to Shimbashi.

If you'd rather keep your bags by your side, then the limousine bus is the best option, followed by taking NEX to Tokyo Station and a cab from there.

Originally Posted by Sanosuke

I second this option -- Nippori station now has elevators down to the Yamanote line from the JR Transfer section or the JR ticket gate side too!