You can set up the LLC anywhere but it will not do you any good because:
1. If you own a property in a state with tenants, property management and rents from the property, you will be considered to be transacting business in that state. This means that you will either need to set up your entity in that state or register it in that state as a foreign entity, which could add to your costs.
2. Setting up your entity in CA also does not make sense because you will still need to register it as a foreign entity in the state in which you own the property, again adding to your costs.
3. I also feel that an LLC may not be the ideal form of ownership if you wish to shelter your non-CA income from CA taxes unless you elect to have the tax treatment as a corporation and not as a partneship. In fact, I would very much prefer a C Corp for what you are proposing.
I do know of people who have owned vacant property in AZ through a non-AZ corporation, but those were vacant properties with no activity that could be construed to be doing business in AZ.
In short, the best approach may be to set up your entity in the state in which you own the property. If you plan to own properties in many states, you may wish to consider a holding company in a tax-free state with that holding company having a subsidiary in each state in which you wish to own properties.
But please consult with your tax advisor and do not take any major decisions based on my opinion or that of anyone else on ant forum.