Unless the two of you are very lucky, that first day in Barcelona will see at least one of you mentally foggy from sleep-deprivation and jet lag. I wouldn't plan more than walking around outside that day; the Barri Gotic and Eixample would be good areas. That means you'd end up with just one real day for sightseeing in Barcelona, which is all the more inadequate since so many of the top sights (assuming you want to go inside them) require pre-purchased--usually timed--tickets to avoid impossibly long lines. You can't put together a maximally efficient itinerary under such conditions, because you don't know how long each site will take or how much time to allow for moving between them. That means you need to build padding into your schedule every step of the way.
As you've discovered, ground transportation in and out of the Basque country is rather slow. To make it worse, the Guggenheim is not in San Sebastian; it is in Bilbao. Travel time by bus (faster than train) will be 2-1/2 to 3 hours round-trip between S.S. and Bilbao. Bilbao is a nice city; i liked it better than S.S. The time you have allotted to that area is minimal but would allow you quick visits to both cities--but not to any of the other interesting places in the Basque Country. And it's at the expense of Barcelona.
Madrid in two days plus a few hours is workable if you don't have a huge interest in art museums (which could take up just about all that time). But what about Toledo and Segovia?
Spain is a large country, and trying to see three different areas of it in what is more like eight days is not going to give you the best ratio of sightseeing to travel time. I'd urge you to drop the Basque Country (because you already have flights in and out of Barcelona/Madrid) so you have more adequate time for the other two areas. You'll still be short, in my view, but it's possible to keep up a pretty brisk pace on a brief trip like this.
I am not a foodie, but El Celler de Can Roca has 3 Michelin stars and is located in Girona, a lovely city with a medieval core on the way from Barcelona to Figueres. Perhaps that might assuage your boyfriend's disappointment about missing Akelare. I have no idea how outrageously expensive it is, or whether it would be possible to get a reservation for June at this point. I'm sure there are other special restaurants within striking distance of Barcelona.
