What about France? O_o
Anyway, I think they began in the city where the Animorphs live, but continue around the world for many reasons (some you already said):
- Military aren't concentrated to their city or their state... and they were close to begin a WW3
- They need to travel as Humans for their cover, so they needa have Pools about everywhere, particulary in the big/important cities
- In David trilogy, some Presidents or Prime Ministers must be Controllers... what if they don't have any Yeerk Pool at home? Will they go to the USA every 3 days? lol
- In the last books, Andalites tell to Ax "How can they (the Animorphs) imagine to hurt Yeerks in destroying only ONE Yeerk Pool?!" or something like that: that means there is many Yeerk Pools all around Earth...
(- When they have the Pool Ship, they ask to other ships and I imagined easily there are other ships (not only Bug ships) from other Pools... don't you think?)
I think step by step, they took one city, another and another... China, Japan, Europa, Brasil, Mexico... may be Australia and other ones... The most important places for them.