Since you only have one week, I recommend to visit either the southern half of Spain, so you have enough time to visit northern Morocco or northern half of Spain, so you can go to Pamplona.
I'll write the most impressive places I can come up with:
===Spain===
Roman:
- Mérida, Badajoz, Extremadura (theatre, amphitheatre, temple, aqueducts, circus, bridge, museum)
- Segóbriga, Cuenca, Castilla-La Mancha (many different ruins, among them an amphitheatre)
- Córdoba (temple, bridge and Europe's 2nd biggest amphitheatre)
- Segovia (very large aqueduct)
- ávila (the walls of the city, they're not Roman but they're spectacular! It's relatively close to Segovia)
- Lugo (the Roman walls, also quite a sight!)
- Tarragona, Catalu?a (Puente del Diablo, also called Puente de les Ferreres, Arco de Bará or Arc de Berà, and amphitheatre)
- Vich, Barcelona (a well preserved roman temple)
Moorish:
- Sevilla (Alcázares Reales, Giralda, Torre del Oro, Torre de la Plata, etc.)
- Córdoba (Mezquita and Medina Azahara which is located north-east of Cordoba)
- Granada (Alhambra, Arabic baths like El Ba?uelo and the district of Albayzín)
- Zaragoza (Palacio de la Aljafería)
===Morocco===
Roman:
- Volubilis (triumphal arch, temple and the "basilica")
Moorish:
- Fès (Bab Bou Jeloud, Bou Inania Madrasa, University of al-Karaouine)
- Meknès (Bab el-Khemis, Medresa Bou Inania in Meknes, Dar El Makhzen, Bab Mansour)
- Moulay Idriss (a village located very close to Meknès and Volubilis)
I highly doubt you'll be able to see everything I just listed, but this way you can choose the places you like best. I hope this helped!
As stated, your plans are too ambitious for one week. You can see part of Spain, or you can see a lot of Morocco: pick one. And you won't find much in the way of Carthaginian stuff, by the way.
If you want to see a little of both, I suggest you visit Sevilla, Granada, & whatever Roman city is around there (I forget: Malaga? Corboda?), and then take a day trip to Tangier. You can't get too authentic in just a day trip (as Tangier is the North African equivalent of Tijuana), but it will give you a taste.
If your trip has to include Pamplona, then write off southern Spain & Morocco, or you'll be one of those silly tourists who spends most of his time on the bus. Instead, see Tarragona (a Roman provincial capital south of Barcelona) and poke around in the Pyrenees. Or, head west and see Leon, Santiago de la Compostela, and/or Los Picos de Europa.
You don't have time for 1% of what you think. In my small town (30K people) which is on the coast we have a Moorish castle, several Moorish signal stations, a Roman Coliseum, multiple Roman aqua ducts and that doesn't even get into the historical battle fields (Christian, Roman, Moors, Spanish Civil War and WW2).
I live here and I am a history buff and I have spent over 2 years looking at the various things (several hours a week) and I haven't even covered 25% of my TINY town.
LOL. A WEEK?
You have time for the running of the bulls.
Clearly, you have no concept of how large Spain is!
I plan on taking part in the running of the bulls in Pamplona, and then would like to spend some time in Spain getting a feel for what life and the people are like there. I'd like to then cross the straits and end my trip in Morocco. I'll have about a week.
Things that interest me are: doing things a little different than most tourists, seeing historical sites (I'm in terested in the Carthaginian era, the Roman era, and the Moorish era) and basically just experiencing the place so I have a good feeling for what life is like there. Also I'm interested in ideas about Morocco. I'd like authentic Morroccan experiences. Where can I go to a walled city with a great market hopefully not too far from the Straits?