How would you distribute your time amongst these cities?

Welcome to the forum, If you’re planning on departing from America on a Saturday and returning on a Sunday— you effectively will have only 7 days. Even nine days is not adequate time for all 3 cities because you’ll lose 1.5 days transferring between them. If you’re going in September, you might choose Madrid and Barcelona which are connected by high-speed trains taking 2.75 hours.

Seville is a little problematic because (1) It averages F 90 degrees during September with 50% humidity. ( October is cooler). and (2). To reach Barcelona by train you must return from Seville to Madrid before going onward to Barcelona. That means 5.25 hours on trains plus more time needed to get to the train stations, pass through security etc. It adds up to the better part of one day. Flying is an option, but again you will use up 4 hours or so—at least half a day—getting to the airport, passing through security boarding the plane when making the transfer by plane.
If you could fly into Seville and fly out of Barcelona on an open-jaw ticket or “multi-city” ticket,—you’d have a more relaxing trip.
So, the nine days actually becomes 8 days in the scenario of flying from Seville to Barcelona.
I was in Barcelona last year for 5 nights and found there still were attractions to be seen that we just didn’t have the time to see. Then spent four more nights on the Catalonian coast. And three nights in Madrid. I had been to Seville on a prior trip.
What you might consider while traveling from Barcelona to Madrid by train, is visiting a city that has become a hot destination since the new high-speed trains stop there on their way to Madrid. ZARAGOZA, once a sleeper city among international travelers, is a very authentic Spanish city that’s the capital of Aragon with its own cuisine. The massive ALJAFERIA PALACE ( 1050AD) alone makes a stop in Zaragoza unforgettable. You won’t be going out of your way by checking ZARAGOZA out on the way to Madrid.

You can buy train tickets up to one year in advance from the high-speed private train company IRYO. The website is www.IRYO.eu/en
www.TheTrainline.com sells train tickets for all the train companies: Renfe, IRYO, Ouigo Espana and Alvia.

There is much to see in those three cities!

For reference, here is the first nine days of RS's recommended itinerary:

Rick’s Best Three-Week Trip to Spain This recommended itinerary gives
you an idea of how much you can reasonably see in 21 days, but of
course you'll want to adapt it to fit your own interests and time
frame. Day 1: Arrive in Barcelona (sleep in Barcelona) Day 2:
Barcelona (sleep in Barcelona) Day 3: Barcelona, evening train to
Madrid (sleep in Madrid) Day 4: Madrid (sleep in Madrid) Day 5:
Madrid, or day trip to El Escorial and/or Valley of the Fallen (sleep
in Madrid) Day 6: Madrid, late afternoon to Toledo (sleep in Toledo)
Day 7: Toledo, evening train to Sevilla (sleep in Sevilla) Day 8:
Sevilla (sleep in Sevilla) Day 9: Sevilla, late-afternoon bus to
Arcos de la Frontera (sleep in Arcos)

https://www.ricksteves.com/europe/spain/itinerary

You can have a great trip splitting your time between two of the cities (and you can have a great time splitting among three cities too!) Be sure to read RS's take at a glance for each of the three cities on this website too. Advising you to overweight any of the three seems like a crime to other two cities since they are all fantastic! Likewise telling you skip one risks missing something wonderful. No matter what you choose, you'll have great time.

Happy travels!

Of the three cities, I preferred Seville. But if you only have 9 full days, I think you should stick with Barcelona and take day trips from there. Girona, the Costa Brava, Tarragona, Sitges, Priorat Wine Country, Montserrat - the possibilities are practically endless. Save Madrid and Seville for your next trip.

Sorry, staying in Barcelona and flying for day trips to Seville and Madrid is not a great idea.
You need way more than a fraction of a day in Seville. Also, don't miss Toledo, the Medieval capital of Spain, just south of Madrid.

Need min. of 3 days in Seville, 2 days in Madrid with one day trip by rail to Toledo.

Agree with the general consensus--while three days might seem like a lot in all three of these places, it really isn't, plus travel logistics eat up much of your time.
Start making your personal list of what to see in each place (plus see what is reachable in the close-in environs as day trips), then decide how many places to include for how many days.

Just as a random example, I have been to Spain five times but never to Barcelona. If I had nine days to spend there, I would focus on the city and its immediate surrounding area, seeing Girona, etc.
For a first-time visitor, Madrid and Sevilla is a common itinerary--though you should choose what you want to see the most. The only mistake would be to try to do too much and spend a lot of time on a train or in an airport that could be better spent. Good luck!

Thank you to all for replying to my first post! You've given me food for thought. I should have mentioned that the trip duration is actually 10 days as my original plan was for 3 nights in Barcelona (our flight hub), then 3 nights in Madrid, then 3 nights in Seville, then 1 more overnight in Barcelona before flying home. My thought was using direct high speed trains between Barcelona and Madrid, Madrid and Seville, then Seville all the way back to Barcelona on the 10th day to save as much time as possible. I'm guessing the trains are a better option then flights?
Also if it's 3 nights in each city, saving one day in each city for a possible day trip, what would be the top options for a day trip from each city? I'm guessing Toledo for Madrid based on responses. What about from Barcelona and Seville? Or would you recommend with only 3 days in each city to just stick to the cities themselves? Thanks again!

Thank you to all for replying to my first post! You've given me food
for thought. I should have mentioned that the trip duration is
actually 10 days as my original plan was for 3 nights in Barcelona
(our flight hub), then 3 nights in Madrid, then 3 nights in Seville,
then 1 more overnight in Barcelona before flying home. My thought was
using direct high speed trains between Barcelona and Madrid, Madrid
and Seville, then Seville all the way back to Barcelona on the 10th
day to save as much time as possible. I'm guessing the trains are a
better option then flights? Also if it's 3 nights in each city, saving
one day in each city for a possible day trip, what would be the top
options for a day trip from each city? I'm guessing Toledo for Madrid
based on responses. What about from Barcelona and Seville? Or would
you recommend with only 3 days in each city to just stick to the
cities themselves? Thanks again!

It makes sense on paper, but once you see the train reality spelled out (see the Renfe website), you might find what we are saying more clear. Anyhoo, I don't think you have time for day trips, and I'd be loathe to add any more train time, but if everyone is set on these three cities, they should also contribute suggestions so you are all on the same page (I feel ancient every time i suggest a guide book, but that is still where the vital info is). If you were flying open jaw, I could maybe see this plan, but having to insert a flight into the next to last day of a trip is just a non starter for me (perhaps a personal problem, lol).
Really do make a list for each place--you might not want as much time in Madrid for example--it really should be targeted to your personal interests.

Day trips options are several. For example, Madrid to Toledo: "Is there a high speed train from Madrid to Toledo?
Yes, traveling from Madrid to Toledo without flying is possible. With around 15 trains running each day, you'll be there in no time - the fastest ones will get you to Toledo in 34 minutes!" A day trip there is common strategy.

There are always tradeoffs-- ah, the tyranny of free will-- and spending time one place means potentially missing something someplace else. I think Rick Steves's advice in his Spain section of this website is excellent. I'd recommend you spend some time perusing that and also watching his Spain videos. You'll get a lot advice on the forum to slow down and smell the roses. Good advice for sure. But I also like to speed up and not waste time loitering smelling roses when there are world class sites to see! Either way, you'll have a great time. Spain is wonderful!!

Toledo is possibly the #1 day-trip option in all of Spain, though it is totally worth 2 or 3 nights for those who have the time. It's much older than Madrid, so it makes a very good contrast. A further advantage is that rail fares between Madrid and Toledo do not vary, so you are not under pressure to commit to the side trip and buy the ticket early before the fare escalates. However, there is one potential issue: Spain is a country where express trains sometimes sell out, and the trains between Madrid and Toledo are no exception. It will be important to keep a close eye on the Renfe website to see how the trains are selling. If you start seeing trains marked "Full", you'll need to make a decision ASAP.

The other top option for a Madrid side trip is Segovia, also a good choice if somehow Toledo doesn't work out.

Barcelona will probably keep you more than busy (many sites essentially require pre-purchase of timed entry tickets lest you spend hours in line), but my top suggestion for a day trip--again, a place where it's worthwhile to spend the night--is Girona. That ticket will be cheaper if booked well in advance, which is problematic with a schedule as tight as yours. You won't want to buy the ticket far ahead of time and realize you will have to miss things really important to you in Barcelona.

I don't think of Cordoba as a day trip from Seville myself, because it has enough to keep people busy for more than a full day, but many people do treat it as a day trip. I give it a high recommendation, but I think you aren't going to have enough time to see Seville well, so you have a tough call here. Not only will the cost of the ticket probably be quite high if you leave the decision till the last minute, but you may find all the practical trains sold out. That doesn't happen all the time, but it happens often enough to be a concern.

Thank you all for your help and suggestions!
Flying into one city and out of another city (we're from Canada) does not make sense financially unfortunately. We prefer direct flights and Barcelona and Madrid are our only options.
Seems to me that the best day trip option might be Toledo (from Madrid) which makes sense to me as it appears that Barcelona and Seville are high on most people's lists and deserve the three full days in each. While in Madrid, Toledo for a one day trip seems doable, leaving Madrid for the other two days.
Appreciated:)