recommendations for itinerary and buying train tickets from Madrid to Cordoba/Seville/Granada

Your itinerary will leave you feeling like you saw nothing except the trains & checking into/out of hotels. Pick 2 places for your 4 days. If you really like art, select Madrid (use the train) & Granada (since you're flying from there.) If not, then I would pick Seville & Granada.

Use Paypal to purchase train tickets on Renfe. They don't accept American cc's.

I agree with Jean, you have too many destinations for such a short time frame.

I'd recommend 1-2 destinations for your 4 days. Córdoba & Granada or Sevilla & Granada or Granada & Ronda.

Here is the information regarding the Tarjeta Dorada (Golden Card) to get train ticket discounts if you're over 60.
Keep in mind that the discount is taken on full price tickets (only), so you may end up saving more money, if you buy your discounted tickets (without the discount card) 60-90 days in advance online.

Here is a helpful website for buying tickets on the Renfe site

Don't forget to buy your Alhambra tickets way in advance ;-)

Have a wonderful trip!

I've bought tickets on renfe.com using an American credit card. You may need the 'Verified by Visa' feature on your card. I would avoid the Renfe site and use the advice from The Man in Seat 61. He recommends loco2.com or trainline.eu.

There is a lot to see in the Barcelona area. Why waste what little time you have in train strations?

Unfortunately, if this is what you are proposing, I fear it is just not feasible ...

Barcelona (6 nights) for meeting
Then, to Madrid (2 nights)
via Cordoba to Seville (1 night)
to Granada (1 night)
to Barcelona for departure

Either,
Spend all 4 nights in Madrid and take day trips to Toledo and Segovia
(AVE train is 2.5 hours each way Barcelona-Madrid)

Or,
Fly to Granada (2 nights) - with a full day for the Alhambra
Train via Cordoba to Seville (2 nights) - with a few hours for the Mezquita
Fly to Barcelona for departure

Thank you all for your suggestions and resources!

I agree, either Madrid or Cordoba/Sevilla. There are direct trains from Barcelona to Cordoba and on to Sevilla that do not go through Madrid, though most require a change in Madrid. I would choose Madrid only if the Prado is a high priority. The must-see for me is the Mezquita in Cordoba. I assume you are going to Granada for the Alhambra and know that you need to buy tickets in advance. I recommend the evening visit to the Nasrid Palaces (if indeed it's nighttime when you're there) and then returning the next day for the entire site - they look so different at night.

The Tripadvisor article is the best. Read it carefully, print it out and use it step by step when you're buying the tickets. Most US credit cards don't work but Paypal is fine. To compare ticket prices, when you use the Renfe site, check "tarjeta dorada" and when you choose a train and click the + box, there's a drop-down menu for prices. Promo tickets are usually cheaper than the TD prices.

If you are over 65, ask for senior discounts at sights.

But don't expect to get the senior discount all the time, because quite often it's only offered to European Union citizens. On the plus side, I was occasionally given the discount once I said I was retired but only 64 yr. old.

I found that in Spain the discounts are for all 65+ or for Spanish citizens/residents (not sure which) only. I've never noticed EU only discounts.

Chani, you and I visited pretty much totally different cities. Mine were all Toledo and points north except for one night in Almagro. Since the OP is primarily going to Andalucía, it sounds as if your experience is more pertinent.