The mosquito-spraying machine.
pldennison ninjaed me by over a decade, but I agree with his choice of the Terminal Tower for Cleveland. It’s no longer the tallest building in Cleveland, since the [del]Society[/del] Key Bank building was built a few decades ago, but it’s still one of the most distinctive skyscrapers in the world. It’s also the primary hub for the city’s public transportation, and the site of one of the swankiest hotels in the city, a shopping mall, and (now) the city’s only casino.
Heinz Field
For Barcelona, my first guess is the Sagrada Familia. There’s many other emblematic buildings and locations, but that’s The must-visit one.
For Madrid, rather than a building I’d say Plaza del Sol. It’s the mental center of the city, and in some ways of the country (Km 0 for our biggest roads is there). A favorite spot for meetups, from celebrating the new year to any kind of protests.
And two other squares for Pamplona (Plaza del Ayuntamiento, although Plaza del Castillo or Paseo [del]Valencia[/del]Sarasate* would also be quite traumatizing) and Tudela (Plaza Nueva).
- Its official name is Sarasate, but it gets called Paseo Valencia about as often. This was its original official name. ETA: according to Wiki, the name wasn’t after the city, but after the lastname of a prestigious scribe who lived nearby when the city walls were torn down and the Paseo was created.
For Saragossa, the Basilica del Pilar. The square containing its main entrances also includes the town’s Cathedral (recently reopened after decades of work) and several branches of the regional and local governments, but if you burned down every building on the square, people would still be howling most loudly about the Pilarica.
What’s with all the 9/11 threads getting bumped recently??? 
For L.A., it would definitely be the U.S. Bank Tower, which was the first building destroyed by aliens in Independence Day.
In Fort Collins, maybe the New Belgium Brewery? Though I suppose if people couldn’t get their Fat Tire they’d just switch to O’Dell’s or some other local next favorite.
I live in DC, I would think that Congress or the White House would have the biggest impact.
Nashville’s Batman Building is the most readily identifiable feature of the skyline and probably would be the target to draw attention. Runner-up would likely be The Parthenon but it’s not as near a heavily populated area and would only bring minor attention by comparison.
Firs off, I would say that the WTC was NOT New York’s WTC, in that there are other buildngs in NYC that would have been more symbolically important, like Yankee Stadium, the Stock Exchange, the Statue of Liberty, or any of several museums, or even the Empire State Building. The WTC was just one of hundreds of office buildings full of typewriters, whose only distinction was that it was the tallest at that moment, and the easiest, rather than the most relevant target.
As for my Texas town, like any other small city east of the Rockies, the county court house is the only building of distinction, and every other landmark would be merrily pulled down if the townspeople thought it would help the economy to do so.
It wouldn’t mar the skyline or anything, but for San Antonio, TX the answer is most likely to be The Alamo.
Here in Austin, the terrorists would be plum out of luck, because the most iconic location has been shut down for decades. It’s too late to blow up the Armadillo World Headquarters because the place isn’t there any more!
They might have to settle for demolishing the Congress Avenue Bridge (poor little bats!) or the Stevie Ray Vaughn statue on Town Lake.
Oh, man, I completely forgot about it!
If wonder if the good people of Ann Arbor still feel the same about Borders as they did in 2001?
Though, really, if Tim Duncan’s hamstring blows out tonight, that will likely cause as much wailing and gnashing of teeth as something happening to the Alamo. 
Just don’t hit the Kentucky Theater during “Rocky Horror” Even ISIS doesn’t tick off a Kentuckian.
The biggest psychological effect? Probably the court house. There isn’t really anything else emblematic of the city, and there’s no real architecture of note. Plus it’s one of the few buildings with more than two floors.
Attacking a certain sign company in a town not far from here might have the opposite psychological reaction, however.
I realize it technically isn’t LA, but I think Disneyland would have the biggest psychological impact.
Within the city limits itself, rather than a building, I’d guess one of the major freeway intersections (405/10 or the four-level in downtown) might be huge.
In Cleveland, it would be the Terminal Tower. When it was completed, in 1930, it was the tallest building in the world, outside of New York, for many years, and still defines the city’s skyline. Its loss would be a major catastrophe.
We had a ‘noobie’ bumping a bunch of them.
Philly
Biggest psychological blow: where our country was founded; Independence Hall
Most damage to a company (& the tallest building): Comcast Tower
I live in a small town of absolutely no importance, and any attack on the town would probably not even make national news. However, I’m 10 minutes away from an Army base that was a major troop deployment center for the entirety of the “War on Terror”, so taking that out would be a pretty major blow to the country as a whole, even though most have never heard of it.
Any one else get the feeling reading through this thread (even 13 years later) that it would be a really bad idea in the wrong hands?