The short answer is, with the exception of Texas, any State who ever broke with Britain has a conceptual Independence Day, though the manner to which these so-called Independence days are noted and celebrated vary widely.
You can blame Rhode Island for starting it. Rhode Island was the first of the 13 colonies in North America that rebelled against the British rule in 1775 and the first to officially declare independence from the British Crown. The other twelve states were: New Hampshire; Massachusetts; Connecticut; New York; Pennsylvania; New Jersey; Delaware; Maryland; Virginia; North Carolina; South Carolina; and Georgia, and so each of those states has an Independence Day too, notional or otherwise.
Texas has one because the original settlers there declared independence from Mexico and were their own country briefly, before siding with the United States and getting involved with the Mexican War, and then deciding they were better off as part of the U.S.
Hawaii has an Independence day because a French ship captain came ashore there in 1839 and claimed what was then called the Sandwich Islands to now be part of France. Then, a British ship captain came ashore 4 years later and he declared the islands belonged to Britain. The crafty Hawaiian King Kamehameha decided to stop this European white-guy claiming madness before any more crazy ship captains showed up, and so he enlisted the help of the U.S. to stop any more claimants. This issue took root and floated around Europe for awhile, and gradually gained widespread support as the European powers wisely decided the only way to settle this was to either have another war with each other, or tacitly admit nobody wins and just give the Hawaiians their independence. The Hawaiians celebrate this day as independence then from both Britain and France. There are no other states that have their own independence day.
While we are on this subject, did you know that there was a city in the U.S. that refused to honor the U.S. Independence Day on July 4th for half a century? During the Civil War, northern forces under Ulysses S. Grant surrounded the town of Vicksburg, Mississippi, a critical Confederate bastion and city on high bluffs overlooking the Mississippi river. After a prolonged siege in which the people of Vicksburg starved and had to live in caves in order to avoid the bombardment, they decided to surrender on July 3rd, 1863. However Grant wanted to underscore the humiliation to the Confederacy and send a powerful message regarding the dominance of the Union, and purposely refused to accept the surrender until the next day, July 4th. Because of the anger and humiliation of this, the town of Vicksburg basically had to wait for a full 50 years, until most of the survivors of that generation all died off, and consequently didn't recognize or celebrate the U.S. 4th of July again until 1913.
