For convenience I suggest you register an LLC in the U.S. State in which you maintain a permanent address personally. You may then use that address as the address for your LLC, citing IRS provisions for a home office.
You must have a street address to register an LLC and the government does not except P.O. Boxes at UPS or similar outlets. You should also check your local city and state web sites for Doing Business As (DBA) requirements and any licensing that may apply.
If you register your LLC with your home state as as a Subchapter "S" "Disregarded Entity" in IRS parlance, you will not pay income tax as an LLC. The revenue and expense write offs will flow through to your personal tax return for U.S. tax purposes
Go to the Secretary of State :Web site in the state in which you live and click on the Business Information area for the forms and fees to file. When you receive your registration, go to the IRS web site and register there.