According to Wikipedia (as well as every other link when I searched), Marlin and Nemo live in an anemone in the Great Barrier Reef, Australia. The GBR is located off of the North Eastern coast of Australia. It's about 1200 nautical miles to Sydney, Australia, off the South Eastern coast. So while they don't have to cross the entire Pacific Ocean, Nemo still has quite a journey.
Disney Pixar's Marlin and Nemo at home (Finding Nemo)
According to this article, as well as other search results, Dory lives with Nemo and Marlin in the GBR, but recalls that she comes from the Marine Life Institute at Jewel of Morro Bay, California, which is 'across the ocean', on the West coast of America.
Disney Pixar’s eternal optimistic Dory (Finding Nemo; Finding Dory)
A fun fact is that Clown fish actually do live (in real life)
in Sea Anemones, in the GBR.
Clownfish make their homes near sea anemones, which protect them from predators. (Image credit: Aleksey Stemmer | Shutterstock)