Or even Shinjuku works. From all of these stations (Shibuya, Shinjuku, Shinagawa), Ebisu is at most around 10 minutes away on the Yamanote line.

Bear in mind that to get to the Westin, you need to exit upwards (escalator available) from the platform, turn right past the turnstiles, take 5 -- count 'em, 5 -- moving walkways, an escalator down, walk for about 3 minutes further, and then a lift up one floor to the Westin. Even from Ebisu station, with significant baggage, I'd consider paying the Y660 for a cab.