10 day trip in late August planned, looking at these 3 cities for destinations. Flights in and out of Madrid.

Looking for your thoughts on the best way to get from one of the other. Flights vs. train. Trying not to rent a car if possible. Though not 100% counting it out.

Many thanks

Sorry I goofed.

Madrid, Seville, Barcelona are the cities we are looking into.

yes, it's very possible the 10 days are counting arrival and departure ? it should be something like this :
Day 1 Anywhere- Madrid
Day 2 Madrid
Day 3 Madrid Barcelona (flying)
Day 4 Barcelona
Day 5 Barcelona
Day 6 Barcelona -Seville (flying)
Day 7 Seville
Day 8 Seville
Day 9 Seville - Madrid (Ave train)
Day 10 Madrid - Anywhere (i don't know where you live )
If you are talking of 10 full days, then I would add the two days to Madrid.

Coming from Boston.

Arriving the morning of 20 August & departing night of 30 August.

Thanks for the suggestion!

You need to be aware that Spain is VERY hot in August. Seville esp is often over 100 during the day. Make sure your hotels have good AC and a pool - since it's very difficult to do anything in the afternoons.