For new grads, do you recommend starting career and living in California, despite the high living costs and high taxes?
I'll reframe this question to change California into the Bay Area because California is a huge state.
I do think it's worth it to start your tech career in the Bay Area if you are very career-focused. You can meet a lot of other ambitious software engineers who are on the same path as you. You can meet software engineers who are on one step above you who can give you the inside scoop on how they progressed in their career.
That kind of information can help you to short circuit making a lot of mistakes that people make. It's not as tangible since there isn't a dollar amount, but it can help you to get promoted faster or learn about a company who has a high growth trajectory.
It's harder to do this remotely because a lot of the info comes out when you start having deep conversations with people outside of work.
Also, the weather is amazing :)
Your salary is generally tied to the cost of living. So typically high cost of living should not be an issue in my opinion. The obvious caveat is that few companies do have a set salary regardless of location for fully remote roles or if you're self employed
Regardless I think SF is the best place to start your career if you have the opportunity to do so
In a vacuum, being in California (the SF Bay Area specifically) is the best for your career. This is especially true now as most top tech companies (especially FAANG) are doing RTO.
But of course, life doesn't exist in a vacuum, so you need to figure out what's keeping you from being in Silicon Valley and decide how important they are. For example, if you need to be close to family and they don't live in Silicon Valley, it's probably best to stay alongside them (there are things in life more important that career).
Here's a great thread which covers this in more detail (I break down the pros/cons of living in Silicon Valley there as well): "How important is location for software engineers?"
Yes, it's absolutely worth it! If your career goes well, the earnings you have now in the early years will pale in comparison to what you'll make in 10-15 years.
Focus less on money and instead focus on building your network now. Focus on money after you've had a few jobs.