Visiting my study abroad student

Not sure about your reference to wanting to leave "on your own time", here are some thoughts.....
Train and bus service is excellent, convenient, relatively inexpensive, dependable and the norm for travel. Sacrificing some schedule efficiency in order to go from point to point with best logistical effectiveness is something worth considering.

What I "read" is your encountering the loss of trip efficiency we all encounter via 1) on day of arrival in Madrid having to clear the airport, get to your hotel, reset and then start enjoying your trip AND 2) the day of departure from Madrid is also a "lost" travel day. I doubt renting a car for an early morning trip along unfamiliar roads to arrive at the airport, return the car and then go through the check in process will gain you any real additional visitation time with your daughter.

HOWEVER, having done this journey with a study abroad daughter based out of Granada, here are some thoughts......

1) what is the flexibility in your student's schedule to join your family? our daughter sought the opportunity to get out of town and travel w us to different destinations. We did have the advantage of having previously been to Granada and you/your student may strongly desire to show you San Sebastian. If she does desire to travel with you then a variety of options arise.
2) what time of the year is this trip?
3) a rental car for a family of five plus a minimum of luggage for the shortage of trips will still need to be a large vehicle. Plus you may encounter one way drop off fees. Plus you will need to get and IDP.
4) it sounds like you may have a travel appetitie bigger than your travel time allows. Are you writing that day one is the arrival in Madrid with day three the departure to San Sebastian? And day 8 is your departure from Madrid to home? Leaving only four days to experience the area around San Sebastian?
5) perhaps you can max the time with your study abroad student by staying in Madrid for two days, then go to San Sebastian and having your student return with you to Madrid on the day before your departure home. This way your family can stay up as late as you like the evening prior to departure, enjoy each others company and not have as much hassle with getting to the airport on the day of departure. Your daughter can then return to san sebastian at her own pace.
Packing uber lite is a big benefit for a trip. Minimizing the urge to "see more, but actually do less" is also of great benefit, but......... One way to max your time in spain is to immediatley adjust your body clock to staying up late and socialize on the time frame of locals. Do not allow your tummies American feeding habits to dictate your schedule. Stay up late! No, later! Pretend you are the student, not your kids.
Enjoy!
BTW, congrats with investing your time money into a study abroad program for your child as this is a great life long rewarding experience.

Cramming 5 people into a car might work but you'll be very cramped. Keep in mind that European cars are much smaller than in the US. Trunk space is almost non-existent even with "larger" cars. You can try and rent the largest car offered, but it won't be a Lincoln Continental if you know what I mean... You could try and rent a small van, but again it might be more cramped than you expect in the US. And even packing light, that is 5-6 bags of luggage plus personal items.

It's a minimum 4.5 hour trip by car on the toll roads (which will be pricey). Assume at least 5 hours with stops.

Are you then adding a 6th person (your daughter studying there) for daytrips? No way will you get 6 people in a car.

There is no way you can leave San Sebastian and get to Madrid for a morning flight. And no way would I ever recommend trying it if it's an afternoon flight. Way too many variables that can have you missing your flight. Plan to stay overnight in Madrid.

Direct trains from Madrid to San Sebastian take either 5.5 hours (2x/day) or 7.5 hours (2x/day). This is a route I would commit to in advance, both because of limited departures and advance-purchase ticket discounts. I can't see much benefit to driving, unless you plan to make stops along the way. For a sidetrip to Bilbao, public transport options run frequently.

When I drove for a few days in northwestern Spain, the motorways around San Sebastian had the most traffic and I was stuck in a traffic jam when approaching the city from the west. In that case, I was actually staying in Hondaribbia and visiting restaurants near San Sebastian, but did not drive into the city itself.

Places that I would consider day trips from San Sebastian include up the coast east into France, Bayonne and St. Jean de Luz make sense.

Going south Pamplona isn't too far and the kids may be interested since it's famous for the running of the bulls. You don't say when you're going. The festival of San Fermin is in July, Pamplona is a zoo then. There is also St. Jean Pied de Port, a small town that is one of the starts of the pilgrimage route toward Santiago de Compostela (Pamplona is along the route). A bit further south of Pamplona is Olite, which has a great castle - one of my favorites in Europe. It's not huge - part restored and part still being worked on. Since they haven't furnished it, you can pretty much explore anywhere you want. There are towers to climb (after you figure out how to get to them). It comes with an audio guide that describes what it was like in the heyday of the Kings of Navarre (this area and part of France).

West is Bilbao, a big city with a great museum.

Southwest you can reach Vitoria easily in a day trip. It's considered the heart of the Rioja wine region - but the Bodegas (wineries) aren't open regular hours for tours, you have to call a day or two ahead to schedule a visit. Burgos is a little far for a day trip but the area (Burgos, Valladolid, Zamora and Salamanca) is what I think of when I think of Spain (add Toledo to that list) and there are three great castles to visit Penafiel (admission also includes the town's wine museum), Coca, and La Mota.

So much to see, so little time.

Here's a little Rome2Rio search I did for your trip: http://www.rome2rio.com/s/Madrid/San-Sebasti%C3%A1n. You can also just go to Rome2Rio (http://www.rome2rio.com/) to do it and some other noodling around on your own.

You will need to click on your transportation choice and go from there for detailed booking instructions for trains and buses, including the number of people, real dates, etc. Rome2Rio does have a Satellite option and you can zoom in to see what you would be driving through in the way of scenery and towns if you decide to drive.

I also tried DB Bahn (http://reiseauskunft.bahn.de/bin/query.exe/en) for the route arbitrarily using 17 March for the travel date. The fastest route leaves at 07:35, arrives at 13:03 and there is one train change in Pamplona. You can go without a train change but the fastest route then takes about 6 hours. You can go to the link to figure that out with your actual dates.

Whatever you do, it has been my experience that arriving in a town after dark is a hassle no matter how you get there. Considering the distance in terms of hours, you may find your family's schedule may not be as free form as you might like.

For everything there is to know about car rental in Europe, go to Gemut.com -- http://www.gemut.com/. Explore their website thoroughly and read the brochure, "What you should know about renting a car in Europe," completely.

Pay particular attention to the section, "The right rental car for you." You are probably not going to like to hear this or to read more detail, but these are a couple of edited quotes:

"MPV (Multi-Purpose Vehicle): A recent addition to European rental fleets has been “crossover” vehicles ... These combination SUV/wagon/van vehicles have created a new rental category, “Intermediate Special.” ... Warning: Some companies advertise these cars for six and seven passengers. Yes, some MPVs come with two folding jump seats but they occupy ALL the luggage space and are not suitable for more than five passengers."

"Vans: ... A seven-passenger vehicle ... simply doesn’t have enough storage space to handle luggage for six persons traveling in Europe. ... Seven-passenger vans have front buckets, a shorter center bench seat or two buckets, and a rear bench. Minivans are fine for four or five people, but beyond that, luggage space is a problem."

Be sure to contact Andy for the information you need if you do decide to rent a vehicle. You are a family of 6 adults, counting the daughter in San Sebastian. It ain't gonna be easy or cheap to rent a comfortable vehicle that will hold all of you, or even 5 of you, and your luggage, but if it's possible, Andy will figure out how to do it.

Thank you for your replies and advice. Realize reading through I left out some information. We are leaving in the beginning of April for 8 days, 4 people plus 1 study abroad student meeting us in Madrid at start of trip. Was able to find an early bird car service through our hotel to get 4 out of 5 of us back to Madrid in time for our flight. ( Flying with miles so didn't mind the cost of car service). Taking 5 people via Renfe from Madrid to San Sebastian. Per my study abroad daughter, no car is needed in San Sebastian and we can get to the places to visit mentioned in your replies via public transportation. Love the rome2rio website and your suggestions were all very helpful! Thank you so much!