What time of year is your trip?
For driving directions and times I suggest ViaMichelin. Although I've never driven in Europe, folks here seem to like VM but feel it tends to be a bit optimistic about times. VM gives 3 routes, two of them at 7 hours and one at 7-1/2. Those times do not include stops, traffic delays, getting lost, searching for parking, etc.
Are you planning to drive through France or through Spain to get to Andorra? There's a 7-hour VM option through each country.
The French route takes you through or near Zumaia/Getaria/Zarautz (small coastal villages), San Sebastian (which you mention so presumably will already have visited) and Hondarribia (larger coastal border town with quite a bit to see) in Spain; and St.-Jean-de-Luz, Biarritz, Bayonne (those all in French Basque Country) and Pau in France. I've only been to the Spanish towns, but the French ones are on my list for the future.
The other 7-hour drive takes you through on near Logrono (probably too close to Bilbao), Zaragoza, and Lleida/Lerida. I've only been to Zaragoza, which is a worthwhile stop. You'd drive within perhaps 30 miles of the charming hill town of Laguardia, but it would come up quite early in the trip. This route is estimated to cost about 25 euros more than the first option due primarily to higher tolls.
The 7-1/2 hour drive takes you through or near the very nice city of Vitoria-Gasteiz (probably too close to Bilbao), Pamplona (worth an hour or two of wandering, but for me not all that interesting) and Lleida/Lerida.
However, I'm confused about your routing plans. Do you have to hit all your stops before Bilbao? Talamantes is pretty close to Zaragoza, so not terribly far off one of your possible Bilbao-Andorra routes.
Even bigger question: Do you have a reason for including Andorra? There is lovely mountain scenery in the area, of course, but the town of Andorra la Vella was no great shakes back in 1972. Since then it has become (reportedly) more or less an outlet mall. Just beyond Andorra are Seu de Urgell and Puigcerda, both of which are very pretty towns. Just a few miles from Puigcerda, back across the French border in the uninteresting town of Bourg-Madame, you can pick up the SNCF Yellow Train, a narrow-gauge RR through the Pyrenees to the fortified (and very touristy) town of Villefranche-de-Conflent.
Jazz is right: There's no Dali museum in Barcelona. It's possible there are some Dali paintings in one of the city's museums. You might check the website for the Museu Nacional d'Art de Catalunya. Otherwise, you have the Theatre and Museum in Figueres and the house in Port Lligat near Cadaques. I have not been to the T&M, but friends really enjoyed it, especially the jewelry exhibition. I found Cadaques lovely in July 2016--all whitewashed houses dripping with bougainvillea. I did not go to Port Lligat, but I've read nothing that makes me think the Dali house is an interesting as the T&M.
The 4-1/4 hour TGV routing between Barcelona and Toulouse doesn't make many stops on the French side of the border--just Perpignan, Narbonne and Carcassonne. Perpignan has points of interest but is not a beautiful-everywhere-you-look town. Narbonne also isn't quite a Class A destination. I skipped Carcassonne because of its reputation for being overrun by tourists, but it is indubitably popular.
Toulouse is handsome and worth more than a full day. Albi would be a good side-trip.
If you lay out your full itinerary, we may be able to help more.