Good place to change money in Madrid airport or train station?

There is nothing at the Seville train station that I can remember. Regardless where you exchange in Europe, the exchange rate will be poor. If you absolutely have to do it, then find a bank in the US with a decent exchange rate and you will do better. Well Fargo is generally around 5% which is good for the US and much better than an exchange bureau in Europe.

You might exchange the dollars for euros in either the Barajas airport or Atocha Train Station in Madrid. I do not recall an exchange booth in Sevilla. In any event, do not take large bills -- no $100! They might not be accepted. I think the airport would be the better place. Perhaps you could pay some down on the day of your arrival at the apartment, and then more each day thereafter. Or, better still, go to your local bank in the states and get them to get the euros for you. Less hassle and likely not that much more expensive.

The airport has money exchange. It's not cheap. In your case, I'd go ahead and get euros from your bank before your trip. You will pay roughly the same exchange rate at either your bank or an airport exchange. Your case, having to shell out a lot of cash on arrival, is the only time I recommend getting euros ahead of time. You might as well get it done here as spend extra time in the airport (and potentially be seen with a wad of cash by a thief). Another option is to open multiple accounts, each with a debit card, and use the cumulative withdrawal limits at an ATM. I don't love that option because I'd worry the withdrawals would cause a fraud alert (even though I told my bank my travel plans) and leave me stuck. That option also leaves you at the airport with a visible wad of cash and a potential target.

You can open chequing accounts in several banks, notify them of your destinations, and be sure enough is on deposit to cover your needs. Having separate cards is good back-up. Or, to be really old-fashioned, American Express cheques are still on sale; exchange them at a Spanish bank in preference to a moneychanger. Some booths advertise "no fee" exchange but may give a poor rate of exchange.
All of these methods will cost you something; that's the banking business.

Well I just went through the process. I got as much as I could from ATM machines, with the overall Euro/$ ratio being 1.34. I did find an exchange place at the Sevilla train station, but it was an awful rate, 1.67. In real terms, this means that in my exchange of $200, I got about 30 Euros less than I would have if I could have used an ATM.

Mark, you just reinforced what experienced travelers have been posting for years - common knowledge - exchange bureaus at airports and trains will give a very poor rate of exchange. Also common knowledge is to avoided all Travelers Checks as they are nearly worthless. Maybe American Express is different but I doubt it. We have always been able to cover large cash needs with two debit cards on two different accounts. Your debit card will have a limit for max withdrawn in a 24 hr period. Determine that time period - generally 24 hrs midnight to midnight US time. Which is mid afternoon Europe. So it might be possible to make a max withdraw at noon and another max withdraw later that afternoon because of the time difference.

When this kind of question has come up before, almost every answer says to withdraw funds from an ATM, either with cards from two different financial institutions, or over a couple of days. It's interesting that, except for Frank, almost every answer is about physically exchanging money. But as Frank says, ATM is really the way to go. No need to pay bad rates or carry a lot of cash. Landlords understand the limitations of ATMs and are generally flexible about letting you pay over a couple of days, if necessary. But the best way is to load two or more different accounts with funds and draw off of both.