On the westside, there are two places:
1. Mizu 212, trendy, rather expensive, upscale place at 212(I think) Sawtelle between Santa Monica and Olympic.
2. (which I prefer) is a little place called Shabu Hachi kitty corner from Ralphs at Barrington @ Olympic. In the 7-11 shopping center. More reasonably priced, better portions, less attitude.
I love shabu-shabu, the restaurant called Shabu Shabu house on 2nd street in Little Tokyo is great but the lines are long. A new place opened a few months ago, Shabu Shabu station, Wilshire Boulevard at St. Andrews (Between Wilton & Western). It's a few dollars more but you get tons more food, nicer atmosphere.