Three of us will spend a week in Spain this June. We plan to begin in Madrid, see Grenada and Seville before flying home from Barcelona.
How would you recommend we travel from place to place? Should we rent a car or rely on public
transportation? Also, we have never been in Spain so please tell us if there are any "can't miss" sights. Thank you.

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Don't forget Cordoba. The Mesquita (Mosque) and Cathedral is good for a day. Travel by train is easy, see Renfe.es website, and pick up reserved tickets at Madrid Airport. Also get Alhambra tickets in advance. From Granada to Barcelona is long train trip, so fly (see Vueling.com).

I can't imagine how you'll be able to see 4 major cities - Madrid, Seville, Granada and Barcelona - never mind anyplace else in 7 days (and are those 7 full days - 8 nights - on the ground? Or really just 7 nights/6days?).

It seems like you should cut out at least one city/area - and then figure out the best travel options depending on your choice of cities.

agreed!
We have been plannig a trip for Oct
including the four cities you have mentioned( some side trips)
excep that we have 18 days.
What is the point in
racing from place to place?

janemv, too many places for one week.