I understand your thought process and agree that the Basque Country is somewhat awkward to get to (given the usually-high extra cost of booking flights in and out of Bilbao), so it makes sense to try to do a good job of that area if you're going to go. My short response to this new inquiry is that I don't see that you really have time for any more destinations beyond one brief stop in each direction. You have nights you must spend in Barcelona, San Sebastian, Bilbao (optional but I recommend it because I like it better than San Sebastian) and Madrid: That's already too much for the time you have available.
Your earlier thread indicated arrival in Barcelona on March 3 and departure from Madrid on March 11. So that's only 8 nights and seven full, non-jetlagged days. It's not safe to hop in a car and drive to San Sebastian on the day after an overnight flight, so it's best to spend at least the first night in Barcelona. You won't be able to see any of the top sights that day unless you're willing to risk sleep-walking through them (and they are rather expensive sights). All the most popular places require purchase of timed tickets in advance. So on arrival day, if you're up to it, you can walk through the Barri Gotic and/or the Eixample. If you're in good shape you can go to the lovely but not overrun Sant Pau Modernista Site, where you should be able to walk right up to the ticket counter and go inside.
Now we're up to Day 2. Do you want to see La Sagrada Familia? Parc Guell? Casa Mila? Casa Batllo? Palau de la Musica Catalana? One of the museums? If so, you'll need another night (at least) in Barcelona.
Let's hypothetically say you're going to sleep in Barcelona on Night 2 and head west on Day 3. ViaMichelin.com offers up three possible routes to San Sebastian, the fastest of which is estimated at almost 6 hours, and that doesn't include stopping, getting lost, traffic delays, finding a parking place or the time required to pick up the rental car and actually be ready to leave Barcelona in the first place. Realistically, it's going to be fairly late when you reach San Sebastian even if you don't stop anywhere except for a quick lunch. You will not have much time for sightseeing in SS that first day.
I think Zaragoza is kind of large to be a practical quick stop on the way from Barcelona to SS. The big-ticket sight there is the Moorish Palace (Aljaferia), and it's not a place you run in and out of quickly. Olite might make a better stop, being smaller, but it has an interesting castle that also takes time to visit. Olite is also famously short on restaurants and not a place you could hope to get a meal at an unsual hour. (Spain eats lunch from 1:30 or 2 PM till 4 PM.) I don't know what to suggest here, but I'm sure someone else will have suggestions.
So by Night 3 you're in San Sebastian. You just have Days 4 - 7 in the Basque Country, because by Night 8 you need to be in Madrid or quite close to the airport. Don't you need all four days to feel as if you've given decent attention to the Basque Country?
ViaMichelin.com estimates the drive from Bilbao to Madrid at about 4-1/4 hours by the fastest route--again with no stops, etc. So if you get an early start you could make one stop along the way. There are multiple possibilities. I like Burgos a lot but don't know how big a hassle parking would be. Also, Burgos is an extremely windy city and we're talking about March, when it could also be rainy. Vitoria-Gasteiz is a lot closer to Bilbao. It has a very attractive hill-top medieval district. I think the nearest parking is a bit of a walk away and might even require a bus or tram ride.
If you have plenty of time to drop the car before your flight on departure day you could spend the last night in the picturesque university town of Alcala de Henares if you don't want to go into the big city for just a few hours. AdeH is relatively near the airport.