Spain or Portugal? Lisbon or Barcelona?

Are you going both places? 10-12 days each? Lisbon is a good central spot for Portugal and there are plenty of things to do in and around to fill 10 days. Of course there will be things you won't see, but that is the compromise. Sintra and Evora, for example, are both easy to do as daytrips. Though with 10-12 days, I would suggest spending a few nights to go to Porto. Barcelona is not a central location for Spain. I personally would not choose Barcelona for that purpose, though I love the city. Madrid would be an excellent choice for 10-12 days, but again for that amount of time I'd also add Sevilla or Granada. Segovia, Escorial and Toledo are all easy daytrips from Madrid. Adding a few nights in Sevilla or Granada would allow you to daytrip to Cordoba and maybe a white hill town.

We did Spain and Portugal this wayarrived Barcelona, stayed at Hotel Inglaterra (would be helpful to you if you use Trip Advisor for comments on these hotels) which was pretty good for the price and location. Did a day trip to Montserrat from here. Took a speed train to Madrid, stayed at Plaza Mayor Hotel (location was key for us and access to public transpo). From here we did day trips to Segovia and Toledo. It was an overnight train to Lisbon to take the bus for a short stay at Fatima (we are practicing Catholics) and then back to Lisbon staying at Residential Florescente (good central location also) to do must sees. A day trip from here was Sintra. Left out of Lisbon- all in all 12 nights.

I agree with Doug, Barcelona is not that Central to other sites. I would do Lisbon / Portugal in the 12 days and follow the RS itinerary.

I would visit Spain. Madrid would be a good starting point, with a day trip to Toledo. Also, I found when researching plane fares that the flights were a little cheaper in and out of Madrid when coming from the US. Maybe you will find the same to be true. After Madrid/Toledo, I would move on to Sevilla, Cordoba, and Granada. Sevilla is wonderful, and I enjoyed it much more than Madrid. Don't spend more than one day in hill towns, they are very overrated! You can see two hill towns in one day if you have a car. I personally would not want to stay at one place and just go out on day trips. You will waste so much time traveling back and forth to one city, and will miss out on much of what these wonderful cities have to offer. The trains in Spain are easy to travel on. We rented a car for a few days, and had no trouble driving around.
I just got back from a trip to Spain and Portugal. We focused on Andalucia and the Algarve region in Portugal, with a quick flight and visit to Barcelona at the end. Barcelona would not be a good choice at all for the idea you posted. It's really far from other cities in Spain.

Why do you say "Lisbon or Barcelona would work better than Madrid"? Madrid would work great as a base for shorter trips.

The answer depends on what you want to see. Madrid is a good base for daytrips to Toledo, Avila, Segovia, El Escorial, and the Valley of the Fallen. You can even see Cordoba as a day trip, using fast trains. Barcelona is a good base for daytrips to Sitges, Girona, Montserrat, and Figueres, among other places. Lisbon is a good base for daytrips to Cascais and Estoril, Sintra, Santarem, and even Tomar or Coimbra (two hours each way). Many, but not all, of these are detailed in Rick Steves Portugal and Rick Steves Spain. I used other guidebooks as well, to learn about additional options Rick didn't mention. Take a look at some, to see what interests you, and only then pick your base cities.