Hi Connie,
I’ve been researching LLCs as well. I’m not an expert but can share a few things that I’ve learned.
Generally, the LLC is registered in the state where the property resides. Also as Jason points out, look into an umbrella insurance policy. These are very affordable. They're typically hundreds of dollars per year, not thousands, and all of the large insurance providers offer them. Your auto insurance provider may be the place to start there. They offer a second layer of protection in addition to the LLC.
To help you understand LLCs further, It may be worth searching on google for "asset protection attorneys" or maybe "tax attorneys" in the state that the property is in, so that you ask them questions about LLCs and maybe have them register the LLC for you in that state.
Generally speaking think of an LLC as a legal entity structure that shields your personal assets, car, home etc. from a law suit against the property inside the LLC. Think of the tax piece separately. Your accountant can probably detail the tax implications of an LLC for you. It'll depend on various factors around your finances and so on.
I’d check out the ‘Financial, Tax and Legal’ forum on the BP site here too. Lots of great posts in there.
Good luck!