Yes, you absolutely can have your virtual office wherever you wish for public facing correspondance.

it is a good idea for your registered agent to be where you are incorporated.

Most of your customers will not know the name of the corporation (unless writing a check to you or become a vendor for you), and when they do, they wont care.

Any official documents will go to the registered agent.

I suggest you also set up your business account with bank of america or wells fargo etc where they have brances in every major city.

Besides the address there are other things to consider when setting up a virtual headquarters I am happy to discuss with you. Set up a call.