All three schools are great. I wouldn’t worry about where their CS departments rank in comparison to each other, because at least in the US, hiring managers won’t make a big distinction. In Asia, I would think UW and UCLA would be better known than Vanderbilt. (I can’t tell if you’re a Taiwanese citizen, or an American citizen of Taiwanese descent. If it’s the former, you’ll need to apply for an H-1B to work in the US, and that’s basically a big lottery that you can’t count on winning.)
When you say you got accepted to Vanderbilt Engineering, does that mean you got accepted into their CS program? If there’s a question about being accepted into CS there, I’d go with the sure thing at UCLA or UW.
Obviously there’s more Asian culture in LA and Seattle. My wife is from Taiwan. Our daughter lives in, and went to school just outside of, Nashville. Everyone in our family loves Nashville, so I don’t think the fact that there’s less Asian influence in the city will be an issue. We lived in Seattle for 2 1/2 years, and couldn’t handle the constant cold drizzle. My wife likes LA. I don’t, even though I went to grad school there.
How much money you make after school will be more influenced by where you work, rather than where you went to school.
It will be logistically easier finding a job if you’re living in Seattle or LA while you’re looking, just because there are lots of tech jobs in those cities. Nashville is less of a tech hub.