Start business in Nevada or Wyoming if I live in California?
Nevada can be a very expensive state to register and maintain a company in. We usually only recommend Nevada when you have a strong nexus with the state, such as physical presence. I would suggest you to consider registering your LLC in Wyoming and not Nevada, as it would be much more cost effective.
You are not required to have a business address in the state of registration. For example, you may use your home address in California as the business address. That being said, if you are going to run the business from California, that by itself would be enough of a reason to consider your business as Californian business, requiring you to register it in the state of California.
As far as business addresses in various states go it might be a good idea to consider a virtual office solution. Most companies offer space in Nevada and Wyoming, so you might want to check that option.