Well, some Narita expresses stop at Shibuya and you could taxi it to the Westin from there for probably about Y1500. Otherwise, you have to go to Tokyo or Shinjuku station and switch to a local train (Yamanote line) to Ebisu. The N'Ex is more expensive than the Keisei Skyliner and many of us had the impression the original poster was concerned about that.

The way to the Westin requiring the least thought is to take the Airport Limousine bus, but the Westin is the last stop and it will take a while and cost Y3100 or so. However, they take you right to the hotel front door.