Hello my friends,
We have a round trip flight booked from the east coast of US to Madrid in late October.  We will be there for 10 days.  I am open to any and all suggestions in terms of an itinerary and what to see and do.  Should we spend a few days in Madrid, take in some of the sights and then fly to Barcelona?  Many thanks.  Also, is it wise to rent a car or depend on taxis and trains.  
Thanks in advance