National Patent

In the United States, the individual states do not have state patent offices; additionally, certain requirements for patent protection, such as novelty, are not exclusive to the jurisdiction of protection. State laws govern trade secrets, if that is an acceptable form of protection for your invention. There are state trademark offices; however, the costs of obtaining a trademark for a single state trademark process often costs the same as a federal trademark: if there were state patent offices, I would not expect substantial cost savings versus federal protection.

While there are no state level patents in the U.S., there is state-specific trade secret laws. Trade secrets can sometime be an appropriate type of protection for certain products/processes. The Coca Cola formula is one example of a trade secret that has stood the test of time and is protected by state trade secret laws. Of course, trade secrets retain their protection so long as they are secret. Therefore if you idea is easily understood by an observer; trade secret protect may not be appropriate.

No way. The federal Constitution provides that Congress enact patent laws, and the courts have held that this pre-empts any similar protection under the law of an individual State. In fact, there was a time when Florida passed a law that protected unpatented boat hulls from being copied, but a decision of the U.S. Supreme Court in 1989 said that the Florida boat-hull protection law was preempted by the federal patent laws and could not be enforced. (See the text of the Supreme Court decision via the accompanying web link.)

That said ... if someone chooses to require by contract that anyone to whom a particular technology is disclosed must keep it secret, then the law of "trade secrets" could come into play. And THAT set of legal principles is separate from the patent laws, and is decided on the basis of State statute or common law as interpreted by the courts of each State.

Trademark can be applied for at the state level and, as another respondent has correctly stated, trade secret law is substantially state law.

Patent law is federal only in the United States.