recommendations for first trip to Spain

I think it is far better see fewer places more deeply than to skim the surface by rushing, especially when you have a number of special interests. So in this situation, skipping Madrid seems logical. Madrid does have a good archaeological museum, though, which aligns with your interests.

Teruel is a very nice small city with interesting Mudejar architecture, but it is practical as a day-trip only from Zaragoza, not from Tarragona or Barcelona. If you decide to drive from NE Spain to Granada, I suppose Teruel wouldn't be too big a detour. (Full disclosure: I've never driven in Europe.)

Since you mentioned liking small towns, I feel I should warn you that Barcelona is not only large, it is extraordinarily popular these days. I loved it and--having returned less than a week ago--am already wondering how to finagle another visit. But there's nothing small-town about it. If you truly prefer small towns and have no interest in modernista architecture, you might consider staying in the lovely and much smaller Girona instead. (Ignore this comment if you want to see the modernista sites in Barcelona.) Day-tripping from Girona to Tarragona would be less practical than making the trip from Barcelona, though.

In addition to Tarragona, Mérida (in Extremadura and not horribly far from Sevilla) has a lot of Roman sights.

Rome2Rio.com indicates that there's not much advantage to driving between Tarragona and Granada (7-1/2 hours vs. 8-1/2 for the train). From Barcelona to Granada the train is actually faster than a car, but it might be worth exploring flights on that route. In both cases the train routes you through Madrid (all RR tracks lead to Madrid, more or less), so I suppose you could make a one-night stop there to see the archaeological museum if you wanted to.

Hi, Spain is a big country, I go to different parts of it very year. If you love architecture Bilbao and Barcelona are definitely the places to go. Salamanca is always on my list as well. Madrid is not.
Malaga is not, but Ronda is nice and the Alhambra is a must. I haven't been to Selville for a while, 3 days kinda seems like a lot in view of your schedule, but I am the kinda girl that spent a week in Bilbao and 2 weeks in Barcelona and still go back as often as I can. Be sure either buy a Garmin chip or rent a GPS.
We always go through Auto Europe, they have always been there for us. Talk to someone, but get an online quote first.

A couple of points.
1. You need more time in Barcelona.
2. Tarragona is an easy day trip. Teruel is not possible.
3. Fly to Granada from Barcelona.
4. Drive from Granada to Sevilla.
5. Is it worth flying to Lisbon for such a short time?

Barcelona - 4 nights
Granada - 2 nights
Ronda - 1 night
Arcos - 1 night
Sevilla - 3 nights
Lisbon or Madrid - 2 nights

I like all the suggestions - I agree that Teruel is out of the way, but the architecture looks amazing.

My husband wanted to "do as many countries" as he could - this trip was his choice, mine is always Italy. :) So we are spending three days in Amsterdam on the front end of the trip and one full day in Lisbon just to get a feel for the place. I expect next time we visit Spain we will do the other side of the country with a better trip thru Portugal.

I think that having the suggestion of flying from Barcelona to Grenada is what I was penciling down in our plans. It seems reasonable and shortens travel time. We both felt we spent too many hours on trains in Italy and not enough time exploring, adding in a short flight seems worth it.

What about train from Barcelona to Valencia to Teruel and then back to Valencia and then fly Valencia to Grenada?

Do you think that is insane? Maybe one night in Valencia or a town nearby.

I would strongly suggest more than one night in Granada. We spent almost a full day at the Alhambra itself, another day just wandering around, and part of a day on a guided walking tour. I don't remember offhand how long we were there, but just one night would have been not nearly enough. Plan at least two nights, even if the only thing you want to see is the Alhambra. That way you can get rested up before heading to your next destination. ¡Buen viaje!

I think it's a matter of either (above), or (below) ...
Perhaps rent a car from Valencia to Zaragoza.
Barcelona - 4 nights
Tarragona - 1 night
Valencia - 1 night
Teruel - 1 night
Zaragoza - 1 night
Sevilla - 3 nights
Lisbon or Madrid - 2 nights

I agree with the previous posts about your allocation of time, but in answer to your question about car rental and driving, in May I rented a car in Granada and dropped it off in Sevilla five days later, after visiting a few of the pueblos blancos. Both pick-up and drop-off were at the train stations. In Granada, we walked from our downtown hotel to the station in about 15 minutes. Driving out of Granada and onto the highway was pretty straightforward. Driving into the station in Sevilla was considerably more stressful, but with GPS, and a couple of laps around the station, I found the rental location. I used Europcar, but Avis and at least one other company operate out of adjacent offices in both stations.

The on-line booking process was easy, and the agent at the pickup station was very helpful, and spoke English pretty well. As for the driving, the highways were all of excellent quality. Some of the secondary roads up into the hills were a little more exciting, but nothing too scary.

If you're stopping in the hill towns for just a quick visit, rather than an overnight stay, I'd recommend skipping Arcos and giving more time to Ronda. You need a few hours to walk around in Ronda, and to visit the bull fighting arena and museum. Arcos has a great view from the top, but if that's all you're going for, I don't think the drive up is worth it, compared to spending time in Ronda. That being said, we enjoyed overnighting in Arcos.

The trip from Barcelona to Teruel via Valencia is estimated by Rome2Rio.com at 5 hr. by car or 5:45 by train. The return to Valencia would be 1:30 by car or 2:45 by train, so starting out in Barcelona, visiting Teruel and returning to Valencia to spend the night would make for a very long day and leave you very rushed in seeing Teruel. I'd want to spend the night in Teruel rather than Valencia.