Stay in Pamplona or stay in Zaragoza or San Sebastian and day trip to Pamplona?

If coming from Barcelona and then continuing on to Madrid, I would say that Zaragoza makes the most logistical sense as a home base to daytrip to Pamplona. Zaragoza's Delicias station has daily AVE (or lower cost AVLO) trains to Madrid.

IMO... the medieval walled city of Olite, which is halfway between Pamplona and Zaragoza, is much more interesting than Pamplona.

Victoria, I think Spain is a large and very spread out country, with many cities and towns containing many wonderful sites and experiences. For a trip limited to two weeks, I would be careful about not spending too much time in long distance travel, and switching lodging, which can easily eat up a lot of valuable time. You can easily spend a wonderful week or more in Barcelona and nearby Girona, Figueres, Tarragona, Besalu, etc. A visit to Madrid could well incorporate time in Toledo and Segovia. Personally, I think Zaragoza and especially the Basque Country of Pamplona, SanSebastian, Bilbao etc. would be better left for another trip that can focus on that very interesting and tasty region.

@Larry, I sadly do not know when I will next visit Spain (I anticipate it will not be for many years due to a variety of circumstances) and Pamplona is a non-negotiable for my friend.

It will be a fast paced trip (that is definitely not going to be to the tastes of everyone else) but we are not looking to cut out this portion of Spain but rather trying to decide how best to navigate the places we intend to visit.

Here's where travel is just so personal, both for your own interests and your circumstances. May I suggest more research?
I combined time on my own in Barcelona with a RS My Way Spain tour several years before Covid. Previously I had also used his Basque tour itinerary to plan my own trip to that region about 7 years ago. San Sebastian remains one of my favorite memories, but for me my interests are always history/culture. I found corollaries between Catalonia and the Basque region for both and think if that interests you and your friend it could work to combine them for that reason. I had a week for both sides of the border there and regional transportation was convenient.
I have not been to Pamplona and also flew- so have only experienced the regional trains and buses. Another option could be to do a little bit of the Santiago de Compostola if you go to Pamplona? Anyway, I always had to travel in July/August as a teacher. When you go there could be a factor, the south was broilingly hot. I appreciated the obvious sites/sights in Barcelona, Madrid, Toledo as a day trip, Granada, Ronda- but if I had to choose I really loved Le Pays Basque! Again this is just so personal.

Pamplona has a more historic feel to it than Zaragoza that is much more modern. They have completely different feels to them. To me, there are no must see sights in Pamplona but it is worth spending a day there. Zaragoza is much larger, has more places to see, and worth a couple days. If you did decide to visit Olite, its historic center is about the size of Pamplona’s. In addition to the very impressive Royal Palace of Olite, there are a couple bodegas within walking distance to the town center. I haven’t been to San Sebastián. It will take about 2.5 hours from Pamplona to Zaragoza, so a pretty long trip as a day trip. If Pamplona is non negotiable, then the decision has already been made. Maybe go to Pamplona and take a day trip to Olite which would be about 40 minutes by rail. The train station in Olite is about a 7 minutes walk from the historic center.

Does your friend hope to see evidence of the festival San Fermin? Out of season, it would be a disappointment. The week of the festival, you don't want to be there as a casual tourist, anymore than you want to be in Siena the day of the Palio.

@Tim, I think she is interested in Pamplona because of San Fermin but otherwise knows it won't be on when we are there (not that I would particularly like to be there during that time for a whole array of reasons).

Victoria, I stand corrected and take back my comment. First, non-negotiable is non-negotiable. Also, this thread has led me to take a fresh look at the map of Spain, and my mind had Pamplona MUCH further west than it actually is, and the distance from Barcelona to Pamplona is actually MUCH more manageable than I was thinking. By the way, I spent a couple of days in Zaragoza and enjoyed it very much. Among other things, it had many fewer tourists than many other Spanish cities and towns.

Victoria, you didn't say when you planning to go to Pamplona/Iruña. Of course most people think of the San Fermines, but they are big fiestas. The patron of Pamplona is St. Saturnino, which is November 29th. December 3rd is St. Francis Xavier, patron of Navarra. There is some moderate festivities during that time.

July post fiestas is know as the "resaca" or hangover. The city is pretty dead then. In the precovid days, from the 15th to the 31st the blue and orange paid parking we free.

Also in Holy Week this is some activity.

I agree with the several guidebooks I read that weren't impressed by Pamplona. Not a bad place, but really a near-waste of a precious day on a short trip. I found both Olite and Zaragoza more interesting. I preferred Bilbao to San Sebastian, and I think the Basque Country would be a bridge too far on this trip.

Like Larry further above, I too enjoyed my stay in Zaragoza, a larger city but very manageable. I stayed at least three full days; maybe four. And while it does have its nice modern parts, it's not entirely modern (as implied in an earlier comment), but has a quaint old historic center as well. (At least it did as of my 2009 visit; I'm assuming that's something that wouldn't have changed.)