Air flights to/from Spain and USA
 

Where are you flying from? That will influence the answers you get.
If you can fly non-stop to Madrid then it may make the most sense to do that. If you must connect somewhere and the travel time & # flights to/from Seville is the same as Madrid, then you could do that.

If it is not too expensive, I recommend purchasing an open jaw, or multi-city ticket. Fly into Madrid and home from Seville. When we did our trip to Madrid and Andalucia, we flew from Marseille (where we were visiting our daughter) to Madrid via Ryanair. Then we used bus and train transportation, and we flew home from Seville. That was easier than backtracking to Madrid, and the price was reasonable. I realize you won't be coming from Marseille, but it worked for us (Boston/Marseille and then Seville/Boston) on one open jaw ticket. Very convenient and reasonable. So hopefully it won't be too expensive for you to fly from the U.S. to Madrid, and then back home from Seville. TAP has flights from Seville to Boston via Lisbon. So perhaps they have the same to your home city.

Tools:

matrix.itasoftware.com

Possibly the biggest collection of air options, so you can run the various combos through the multi-destination search function with your home airport. It's quite possible that the multi-city ticket across the Atlantic will cost about the same as a simple round trip so you save the expense, and the time, of travelling back to your arrival point. ITA does not make reservations so you go to the site of the airline that suits you.

www.skyscanner.com is good for flights inside Europe on budget lines. But when you are sticking to one country it is probably better to travel by rail.

Lots of help here: www.seat61.com

It seems you are doing this in a vacuum.
Have you actually looked at what kind of flights you can get at what prices? If some options are dead on arrival, why bother keeping such an option in your head?
Have you looked at the ground transportation to go with each option?
Have you looked at what kind of venues go with each option? You don't want a routing which places you in the city when the venues of interest are closed.
And finally, have you looked at what accommodation options are available with each flight? Some people don't think about this, books flight and realize they must stay in the city with inflated accommodation prices because of a big event they didn't think about finding out.

From what city in the US can you fly N/S to any of these cities OTHER THAN Madrid?????

No city! At least I never found one, and I fly out of JFK, which would be the most likely to have a non-stop to those other places.

YOu can't fly nonstop to Madrid from most cities in the US, either. There is no way you are going to fly nonstop to a small city like Seville from the US.

The choices presented by the OP do seem the only obvious ones if those are the main cities they are visiting, where else. And they do present open-jaw options. There are a lot of flights to/from Malaga within Europe but they aren't going there so why would they fly in or out of it.

I've flown into Seville from the US, used to connect in London but I think BA stopped doing flights to Seville from there, not sure, last time I did this I went from US to either AMS or BRU to connect. I think you can on Air France through CDG also but I prefer AMS/BRU for easy connections.

You don't say where you're flying from, but I flew out of JFK in April to Seville (change planes in Madrid) and returned from Madrid, a direct flight, on Iberia. Very good experience with Iberia.

The logistics would be easier to fly open-jaw (as other posters have said) into Seville or Cordoba, and return home from Madrid.

I'm not aware of any nonstops from Seville/Cordoba to the US, so you'd have to change planes in a European hub. Coming home, that generally means an early-morning flight from Seville to the hub, as most westbound transatlantic flights leave Europe in the late morning. Flying home from Madrid eliminates that additional headache.