Well, most large cities aren’t going to have airports within their actual boundaries, are they? Urban real estate is expensive, and airports aren’t small.
Cincinnati Airport isn’t even in the same state as Cincinnati (it’s in Kentucky).
The nearest customs station, alas, is over in Nevada. 
Many do, including New York (JFK and La Guardia), Los Angeles, and Chicago. But you do have a point; the question in the OP should really be limited to metropolitan areas without ready access to an international airport, rather than cities that don’t have an international airport within the city limits.
I’m pretty sure I’ve seen international flights out of Providence on Family Guy.
Okay, so, um… I got a little carried away.
I scraped Wikipedia, collecting cities, populations, airports, and lat/lon coordinates. I threw out airports that didn’t have “International” in their name, as a start. I then calculated, for each city, the airport that was closest (by the Great Circle distance).
Here’s a figure showing the scatter of airport distance versus city population.
Here’s the processed data (city, population, nearest airport, distance to airport in miles).
Here’s the data sorted by distance.
This definition of “international airport” leaves Boise at the top of the list, with seventeen cities beyond 100 miles away.
If anyone is interested in paring down this Wikipedia airport list to a proper set of international airports (rather than my own paring down based on name), I’d be happy to rescrape and reprocess.
New Orleans International is actually sits on land that is owned by New Orleans, although it’s entirely surrounded by the City of Kenner. It was a trick they pulled so that City of New Orleans could collect parking tax and sales tax on the overpriced shops and restaurants in the airport.
In exchange, Kenner got to do traffic enforcement on the airport access road which had a ridiculous speed limit of 35 MPH for years.
But you’re right. MSY serves the New Orleans area as well as the Baton Rouge area. From my house in the New Orleans Suburbs it takes about as long to drive to MSY as it would from a southern Baton Rouge suburb.
Of course, they probably have flights to every airport in the world.
I actually flew into Providence once. It’s a small airport. It reminded me of Islip in Long Island, NY.
It also reminded me of the airport in Portland Oregon, which is an international airport, but it struck me as being small. Maybe I didn’t see all of it though.
Providence has service to Toronto. In fact, it’s the very first destination mentioned on the airport’s website under “Airlines.”
I have personally flown direct from Toronto to Jacksonville and back. So at one point they did. Perhaps the flight is offered only during certain times of the year.
They shut down one of the terminals a few years ago, so probably it was that one.
Although the name of the airport serving Providence is T.F. Green State Airport, it is indeed an international airport. There is a customs facility on the lower level, with a dedicated stairwell/elevator to Gate 8. Air Canada has multiple daily flights to and from Toronto, and we* have received, for many years, seasonal charter service to and from the Azores that uses the customs facility. It was built in 1996/98 with the new terminal and terminal expansion project. There was a previous customs area in one of the hangars, part of the old, old terminal.
The Terminal Map shows the customs area (Federal Inspection Station, or FIS) on the lower level. It’s really a lot bigger than the map shows, that’s really just the exit from FIS into the baggage claim.
*Disclaimer: I have been a proud employee of T.F. Green Airport for many years, and get snippy when people dis my airport.
Believe me, I am not dissing your airport at all. It is MY home airport of choice as well and I think it is great. My daughters flew out of it last night. Whenever someone suggests that I have to fly out of its big brother competitor, Boston Logan, I puke in my mouth a little. I didn’t know Providence had any international passenger flights until now though.
We can also go by the U.S. Census Bureau’s list of metropolitan statistical areas. As far as I can tell, the largest MSA on that list without an airport currently having scheduled international air service is the Virginia Beach/Norfolk/Newport News area, at #36 on the list. Austin (#35), mentioned above, has seasonal service to Cancún, so it satisfies our criteria for only part of the year. The largest metro area without any intercontinental air service (taking Central America and the Caribbean to be in North America) appears to be Riverside/San Bernardino/Ontario (#14); if you consider that to be part of the L.A. area, then the next largest is San Diego (#17).
On that list you have:
Bishop is the airport serving Flint, Michigan. There are at least two international airports closer to Detroit, including Detroit Metropolitan Wayne County Airport, which was the first place I ever visited in the U.S., having arrived there on a flght from Sydney, Australia, via Osaka, Japan. (It no longer has flights to Australia, but it still has flights to Asia, Europe and South America).
The other airport that’s closer to Detroit than the Flint airport is Windsor Airport, but that probably doesn’t count, since you have to make an international trip to get there from Detroit.
They don’t have “International” in their name, so they aren’t in my list. I’d be happy to repeat the exercise if someone has a clever way of identifying the international airports in the Wiki list of US airports, but until then, I’ve only got the names to go on. (DTW is not the only conspicuously absent airport, but I wasn’t about to go through case-by-case.)
Similarly, several years ago, I was on a flight from Atlanta to Jacksonville which then went on to the Bahamas (I got off the plane in Jacksonville). Perhaps this route is not offered any longer, either.
That list also has Newark (which is in New Jersey) as the closest airport to New York City, despite the fact that there are two other airports inside the city limits of NYC.
EWR’s coordinates are closer to New York City’s coordinates than JFK is. (LGA isn’t international according to the disclaimers above.) The coordinates for NYC point near Little Italy, which is indeed closer to EWR. (Sure it’s in NJ, but it’s right over the border rather than clear on the other side of the city.)
Cities are not points, so obviously the list is only useful for distances somewhat greater than the typical size of a city.
Well you have to explain to me how in the late mid seventies I flew from Toronto to Jacksonville in January on a return ticket only to find that not all of Florida qualifies as winter warm spot. I took a bus to Miami to spend a few days on the beach.