SELF IMPROVEMENT

unclaimed land
After a group of reefs were artificially heightened, the Republic of Minerva was declared on them. Later it was annexed by another state, because they "long served as fishing grounds for the Tongan people and have long been regarded as belonging to the Kingdom of Tonga".

For a somewhat different category, it could be possible to claim abandoned buildings (as the Freetown Christiania did in the midst of Copenhagen), and perhaps achieve a form of limited independence. In this example, it worked. This goes way beyond squatting unclaimed property

A project named Microna attempted to build a town in Nevada, that is currently listed as a ghost town. They secured land, but didn't do much beyond minting a few coins. It reportedly failed due to the complexity of municipal zoning unclaimed property laws

And there are many odd locations with an odd political status, like this one or this one.