The leg of the Gyre closest to Japan – the Kuroshio current – begins right next to Fukushima:
While many people assume that the ocean will dilute the Fukushima radiation, a previously-secret 1955 U.S. government report concluded that the ocean may not adequately dilute radiation from nuclear accidents, and there could be “pockets” and “streams” of highly-concentrated radiation.
Physicians for Social Responsibility notes:
An interesting fact for people living on the US west coast is also included in the UNSCEAR [United Nations Scientific Committee on the Effects of Atomic Radiation] report: only about 5% of the directly discharged radiation was deposited within a radius of 80 km from the Fukushima Dai-ichi nuclear power station. The rest was distributed in the Pacific Ocean. 3-D simulations have been carried out for the Pacific basin, showing that within 5-6 years, the emissions would reach the North American coastline, with uncertain consequences for food safety and health of the local population.
No need to get too worried. The abundantly cautious might simply opt to take a geiger counter to the beach to check for pockets or streams of radiation that day.