My husband and I are flying to Barcelona in June for about 13 days. We fly out of Madrid. Should we rent a car in Barcelona and drive to Valencia or should we skip Valencia and fly/train to Granada or Seville,rent the car and spend more time there? Are Valencia and that drive worth the time? Is there much to see?
For our return home, is it better to take the train to Madrid from Seville rather than driving to Madrid to return the car at the airport? We were planning on staying at least the night before our flight home in Madrid.

If you want to visit Barcelona, Sevilla, Granada and Madrid in 13 days you'll barely have enough time for these places. I'd recommend 5 nights for Barcelona (minimum) if it's your first entry point as you'll likely be jetlagged for 1 day. This will give you a good taste of Barcelona but probably not enough time for any daytrips. From Barcelona I'd fly to Granada and spend 2 nights. Then bus or train from Granada to Sevilla. Spend 4 nights in Sevilla and do a daytrip to Cordoba. (alternatively you could visit Sevilla between Granada and Sevilla). Then take the AVE train to Madrid for 4 nights and do one daytrip (Toledo would be my personal first choice). These are all my personal minimums and total 14 nights. So unless you wanted to give up one of the locations to include Valencia I don't see how you'd fit it in - unless you want a very fast paced trip.

If you only want to spend your final night in Madrid and are not interested in visiting then I'd probably visit Barcelona (4-5 nights); train to Valencia (2-3 nights); fly to Granada (2 nights); bus/train to Sevilla (4 nights); train to Madrid (1 night).

These are difficult to answer--have you read about Valencia and is there some reason you are considering it? If it was me, I would spend half my time in Madrid and half in Barcelona, and I would use the train to travel between them.
Have you been to Madrid before, or are you just not interested in much time there?

You itinerary is far too busy for only 13 days. I'd do what CathyM recommends, especially if you are arriving in Barcelona after a long international flight. The first day will be shot.

You'll need the time on the first day to adjust to the time change and dining hours, lunch is served between 1:30 and 4:00 and dinner usually begins after 9:00, much later in Madrid, but you should not both in same day.

Based on where you want to go, do and see, I wouldn't recommend renting a car.

Thank you all for replying. We do this on every trip...try to see too much in too few days. Valencia was just on the way if we drove from Barcelona to Granada.
CathyM, I like the way you divided the time up among 4 cities. I will play around with that idea given the things we want to see in each place.
We would like to see something of Madrid, but plan on returning to Spain to visit places in the north in not too long and could include it again then.

We are planning a 10 day 2 person trip to Seville-Cordobs-Granada area start of October. We are hoping to fly to Seville - and no plans except to start and finish there stopping over for a few days in each of the other places. Not a car driver. What are the buses and trains like? Is there a chance of hiring a motorised bike perhaps? Given that it's late in the season how easy would it be to just show up and find a hotel(preferably authentic!)wirh vacancies? Possibly take Algeciras ferry and stop over in Morocco briefly if time allows. Any suggestions welcome.

HI @Drebin- I was wondering if you had a trip report or could share how you divided your time between cities and your transportation. I'm flying into Barcelona and out of Madrid (14 days) end of September, and we too like to rent a car and drive. Would love to know if the drive from Barcelona to So. of Spain is nice and worth it. Thanks in advance for your insight.

I agree that with your stated desires, stopping in Valencia, which has fewer interesting sites (unless something there "speaks" to the traveler in you), would be taking away from your main goal of the "Big 4" in 13 days.