The route we drove was Barcelona, Montserrat (for a day stop), night in Zaragosa, day stop at a great castle in Olite, night in Pamplona, night in San Sebastian but then we headed in a different direction (through Vitoria toward Burgos, Valladolid, Zamora, Salamanca, Avila, Segovia, and Toledo).
I chose to skip Andorra. Based on reviews I'd read, it didn't seem like anything I'd want to visit.
Paradors are great. My Father-in-law stayed in paradors when he was in Spain and loved them. We stay in budget lodging. In Spain, we stayed in anything from adequate to nice rooms, probably half were under 50 euro for a double, two-thirds under 65 euros. The most I paid (other than Barcelona and Madrid) was 117 euro for a beautiful room in San Sebastian. Paradors are more like 300 euros.
I personally don't like staying in Madrid and taking day trips out. The advantage of doing it this way is not packing and unpacking. The disadvantage is Madrid is way more expensive than the surrounding towns and cities. Lodging is expensive and not that great (unless your budget is very high). Same for eating, food is expensive and uninspiring (again may be better at the very high end). Madrid is also a new city, it has no charming old center - but does have a world class art gallery, El Prado, and some really nice parks.
I feel it's better to stay outside Madrid unless you plan to spend your day in Madrid. To me it's cheaper, you will have a nicer room, better local food, and warmer people - plus be close to the sights you want to see.