Even Las Vegas?
another vote for doesn’t count.
Part of it is because you don’t really go there on purpose. It just happens to be where the plane decides to land you. Nobody choses their layovers.
That’s similar to what I was going to say, which is that only final destinations count (IMO). I haven’t really thought it through, but that’s what kept coming to mind while reading this thread.
If you drive across one state on your way to another, or stopover in one state’s airport on your way somewhere else, you can’t say that you’ve been there. Yes, in the strictest sense of “been there” you were, but when most people ask “Have you ever been to XXX,” that’s not what they mean. Business trips that take place entirely on airport property are tricky, but I’d tend to say that they do count because they meet the “final destination” standard. I have changed planes in Atlanta a million times, but would never say that I’ve been to Georgia.
I also say that if you can’t remember being there, it doesn’t count. I don’t remember either Texas or Germany from when my father was in the Army, so whenever someone asks if I’ve ever been to either place I always say, “Not since I was a baby.” I don’t remember California from back then, either, but my father took me there in February so now I can say that I’ve been there (which is good, because I was born there!). On that flight the plane stopped in Chicago on the way there: we never deplaned, so there’s no way I’d say that I’ve ever been to Illinois.
I’m kind of tough on myself about this stuff, though. I went to a 3-day conference in Nashville a few years ago, but only left the hotel to walk next door to the mall. I don’t think of myself as having really been to Nashville (but I do get credit for the state of Tennessee, because my father used to live in Chattanooga and I visited him there once). Likewise, I spent a Monday afternoon on Bourbon Street in New Orleans once (while on a business trip to Biloxi), but whenever I’m asked if I’ve ever been there I say, “Not really.” I have the bar and strip club experience, but there’s so much more to NO than Bourbon Street and I never saw any of it.
On Zeldar’s scale I’d say only #1 or #2 counts, because #3 or #4 could happen during a drive-through or stopover. Of course, there are ways to wind up somewhere deliberately other than #1 or #2 that would count, but that’s my answer given those choices. 
So in my two earlier examples, I now have the magic sense of knowing what New Hampshire and Delaware are like?
Let me tell you, the 2 miles of Delaware I saw sure seemed exactly the same as the MD shore from what I could tell.
Lots of places of all states look exactly the same as some places of other states. So what? What difference does it make what the part of a state you have been in looks like?
Plus, not all airports are alike. Boise is a far cry from Logan.
Hehehe. I had a stopover once in Houston. I never really cognized where I was stopping over. The whole thing was a last-minute trip with very little planning and so I wasn’t really thinking about the details. The plane landed, I got off, and I tried to remember when to get back on. No problems.
It was one of those “you can buy a packet of peanuts for five bucks” flights, so I was starving and went to the Taco Bell Express right in front of my gate.
They cashier opened his mouth to talk to me, and I couldn’t figure out a word he said. I had to ask like three times.
Then I realized I was in Texas, it all came together, and I understood everyone was talking like a Texan. I didn’t have any more trouble understanding people.
It was bizarre.
I don’t count them.
It doesn’t affect my count, I have been to all the states I where I have had stop overs. It does cost me Israel from a 3 hour stop in Tel Aviv, but I refuse to count a country without seeing part of it.
For the purposes of simply listing states you’ve been to, the airport counts. After all, if you weren’t there, where were you?
The airport caveat should always be mentioned, though. If someone were to ask me if I’ve been to Minnesota, I wouldn’t say “yes” and I wouldn’t say “no”–I’d say “only the Minneapolis aiport.”
It doesn’t count, and it stinks. I’d love to tell people I’ve been to Japan and Germany, but the Tokyo and Munich airports just don’t cut it.