From my perspective, your rough itinerary has you moving a bit too fast, especially given the length of your trip and that there are 4 of you. Will you be sharing one hotel room, with just one bathroom? How quickly can you get four people out of your lodgings every day? The places I'm most worried about are Barcelona (where so very many sites require timed tickets, which make for less-efficient sightseeing) and Seville. I note the omission of Toledo, which is magnificent. Cadiz is a worthwhile stop (I've never bothered with Gibraltar), but it doesn't hold a candle to Toledo.
I would certainly skip Santander. It has a lovely beach (but so does San Sebastian), but most of the city burned down in the 1940s, so it lacks the historic atmosphere you'll find at most other stops. It's not a bad place, but that time could be used elsewhere.
Santillana del Mar is a very popular medieval village but tiny. It really doesn't require an overnight stay unless there are other things you want to do in the immediate area--for example, the caves with prehistoric art, if they are still open to the public.
Gijon has a small historic area and some attractive late-19th-century architecture downtown, but there's more bang for the buck, time-wise, in Bilbao, so Gijon wouldn't make the cut for me on a one-month trip. I like Bilbao a lot, much more than San Sebastian, though SS does have that wonderful beach (but not necessarily beach weather on any given day). Bilbao has a large, comparatively non-touristy medieval district. There's frequent bus service between SS and Bilbao, so it's possible to stay in one of those cities and visit the other by public transportation if you want to. There's also regional train service through some really pretty countryside (though definitely not as dramatic as the Picos de Europa), but it is much, much slower than the bus. Other places in the Basque Country your son may want to research include Hondarribia (cute fishermen's district down at water level and medieval area on the hill) and the three coastal towns of Zarautz, Getaria and Zumaia. I walked along the coastal road between two of them but no longer remember which two. I haven't been to Guernica or Lekeitio, which are other places of tourist interest.
Pamplona is another place that didn't excite me. I think you'll find the guidebooks mostly agree with my point of view. Unless you're there for the running of the bulls (when hotel prices skyrocket), it's a fairly ordinary town. You can probably see the entire (small) historic section in half a day. If you go, make sure to see the life-size statue of the running of the bulls; that I was glad I saw. Personally, I'd use that time elsewhere, but I realize that's a tough call if there are big Hemingway fans in your group.
Santiago de Compostela is certainly worth it, but there are a bunch of places of interest between Barcelona/San Sebastian and SdeC. Some of the major ones are Burgos, Oviedo (this being rather near Gijon) and Leon. Just within Galicia itself there are charming towns and cities to see. I wouldn't cross the bulk of northern Spain to squeeze in just one or two nights in SdeC, especially if I were going to Madrid and didn't have time for Toledo.
I haven't yet been to the Balearic Islands or to Sardinia (which is Italian), so I'm definitely not going to disagree with Carlos. However, my research for a forthcoming trip indicates that Palma de Mallorca is the most aesthetically interesting city in the Balearics, with some modernista architecture (which I love). Mallorca is also the island with the most interesting terrain. So it's definitely the main one for me. Your interests may differ.