Three courthouses. Starting from the mainland end they are:
Plantation / Tavernier at the ~1/4th point along the island chain.
Marathon at the ~2/3rds point.
Key West at the far end.
Those towns pretty well contain the bulk of the populace, and the other concentration, in Key Largo / Islamorada closest to the mainland, is quite near Tavernier / Plantation.
Although the definition of “county” has been redefined over the years, if we include any jurisdiction with a courthouse - in the province of Quebec, both the islands of Montreal and Laval have their own courthouses.
It looks like “Les Iles de la Madeleine” also have their own courthouse. It’s a small group of islands in the Gulf of St Lawrence. (pop. 12,000).
The province’s largest island (Anticosti) has a population of 177 - too small for its own courthouse.
We have the Isle of Wight, Orkney, Shetland and Comhairle Nan Eilean Siar (the Western Isles Council).
The Channel Islands and the Isle of Man are self-governing Crown dependencies, so not part of the UK, though not totally independent.