New Jersey LLC v. out-of-state LLC for renting out our apartment
Technically you could register the LLC anywhere, but this way or another it has to be also registered in New Jersey (its called Foreign Qualification, or just forming a Foreign Entity).
You can read a previous question about owning real estate in California with a Wyoming LLC to get a better idea. Also, there was a good question about which cases would require you to register a Foreign Entity and which wouldn't.
As such, for the purpose of renting a property, it might just make sense to register in the state where this property is located.