But I’ve been to Oklahoma. 
I did not know about those! I suppose that India would still fit onto the “two states” list if those archipelagoes were actually states.
Japan’s northernmost island, Hokkaido, constitutes a single prefecture.
Or does this not count since Japan is entirely islands? I’m not entirely clear on that.
Many unitary (i.e., non-federated) countries in Europe have autonomous regions (or similar terminology) with more far-reaching self-administration rights than the administrative units that make up rest of the country. In other words, they have more extensive rights than a “normal” administrate unit. Typically, they are regions with a population that is ethnically, historically, and linguistically distinct from the majority, or which are simply geographically so far away from the rest of the country that it makes sense to accord them wider rights of self-determination.
Examples are numerous and include, among many others, Sicily and Alto Adige in Italy; Faroe and Greenland in Denmark; or Madeira and the Azores in Portugal.
But I’ve never been to me.
As for the OP, Argentina is made up of 23 provinces, one of which is the Argentinian half of Tierra del Fuego (the other half is Chilean). It also includes Argentinian territorial claims to other areas that are not internationally recognised (in Antarctica, and to a number of South Atlantic islands that are controlled by the UK, most importantly the Falklands).
Trinidad and Tobago
Well, you’re the reason God made Oklahoma.
Finland has 21 first-level administrative regions, exactly one of which (Aland) is an island.
Jersey Shore, PA is closer to Lake Erie and Lake Ontario than to the Atlantic Ocean.
In general, island-only countries do not count. However, if the country is mostly on one large island with multiple regions on that island but it also has a different island that makes up a region, then that would be a situtation that has the look and feel that I’m looking for.
At first glance, this would be such a situation, but Tobago is considered a ward, whereas the others are regions. It does have a different governmental structure than the regions.
Yes, I looked up Finland before posting. Åland is an autonomous region, so that disqualifies Finland. It’s also an archipelago rather than a single island, although that doesn’t disqualify it.
Looks like a good one.
Two of Equatorial Guinea’s provinces are on the island of Bioko.
Singapore?
Indonesia: Bali, the Bangka Belitung islands.
India has about 1400 islands
None of them are states though.
True. I was responding to the answer about the Union territories of Andaman and Nicobar / Lakshadweep (just pointing out that there are more than 2).
In terms of big islands, I think Goa (state) would have the most.
Interesting. I’ve idly wondered why it was called Blue Island, but idly enough that I never looked it up.
The legal name used to be the State of Rhode Island and Providence Plantations, but it was shortened to just Rhode Island in 2020.
Providence Plantations was the site where Roger Williams went after being expelled from Massachusetts. It’s on the continent, not an island.
Rhode Island is where the super-wealthy town of Newport lies. In 1644 it joined up with Providence Plantations to form the Colony of Rhode Island and Providence Plantations.
Rhode Island is also called Aquidneck Island and people keep trying to give back its Indian name.
Nobody outside of the state cares one way or the other about any of this history.
Yemen. Divided into 21 “governates”, and one “municipality”. One of the governates is the the Socotra Archipelago (22 on this map):
There might be a rub here in that while Socotra is recognized as part of Yemen, there is an ongoing civil war, and Socotra is under the de facto control of a separatist faction.