I could think of one in Chicago off the top of my head that is probably familiar to at least Midwestern beer drinkers: “Goose Island.” (Although it is an artificial island, in that one side of it is from a canal, so I don’t know if that counts or not.)
I don’t think the old historic ranch down at the south end of the island is inhabited anymore, but I think there’s some sort of caretakers who live at the north end of the island. Of course there is also the issue that the lake level often makes the island a peninsula, which I think is the case more often than not these days.
Well, Idaho has an inhabited island at 43.63095, -112.068
Pretty stretchy indeed. Yet Wyoming does have an island with a cabin that is inhabited at times. And is even famous for who stays in it.
North Dakota has a whole town on one (Fort Yates). Although it appears that a causeway was built to connect to the island. Not sure if that disqualifies . . . .
Good enough for me!
And Jackson Island in SD looks inhabited! 45.71289, -96.73100
Fort Yates also has the issue of not being an island during periods when Lake Oahe is low, which I think some years is the whole year. I’m not sure if there’s a way to do this in the browser, but with the actual Google Earth program you can look at older images and you’ll see that some years there’s even crops planted in between the island and mainland!
Aha! An inhabited island in New Mexico! 34.94526, -106.677118
Well, sort of. I bet a homeless person or drunk has slept on it before.
Damn, why won’t people build on those nice river islands in the Rio Grande? Your house probably won’t wash away more than once every 5 or 6 years.
Okay, this spot at 36.11690, -106.05271 in NM is on a piece of land between the Rio Grande on the SE and an irrigation ditch to the NW. I think it’s a house because there’s a garden and what appear to be kids playground stuff by it. Surrounded by water, at least when the river’s up a bit more, though you can see water in most of the ditch.
By that standard, I’m fairly sure we can get Nevada with Reno’s Wingfield Park. I think that’s a pretty scary part of town after dark.
I like it!
Here’s a little artificial island in NV between the Truckee river and a canal built for the river dam. Lots of homes on it! 39.58629, -119.37704
I suspect we need to look in Wyoming or Montana or North Dakota for a state with no uninhabited islands.
Nah, we’ve already found islands that pass for inhabited in those states, on the first page of this thread. 
A state with no uninhabited islands? I don’t think even Hawai’i manages that.
Nah, it’s downtown. Maybe some homeless but very central to everything, and a couple blocks from the police station etc. anyway.
Anaho Island explicitly forbids humans.
I think the case for California is much stronger (to SW), but technically the waters of Lake Tahoe are shared, and Fannette Island was inhabited but I think not semi-permanently anymore.
Lake Lahontan might’ve had some cave people. 
Plenty of people live on Catalina - so California is done.