Portugal in May 2019

First, don’t pick up the car until you are leaving Lisbon. Driving in Lisbon and parking are very challenging.
I think you are being overly optimistic about what you can see between Lisbon and Porto. Even though the history’s are very different, Alcobaça and Batalha have similar architecture. You might want to read up on them and visit the one with the most interesting (to you) history. Alcobaça is my preference.
The one city of note that you are missing is Coimbrã. It is quite lovely and the university library is spectacular. Go Walks does a great walking tour that gives you a good overview of the city for a great price. If you can fit it in, you likely won’t regret it. I much prefer Coimbrã to Obidos.
There are a number of small group tours of the Douro from Porto. It’s s long day, but enables you to get a glimpse of the Douro and wineries without the hassle of driving.
Evora is worth two nights to give you time to do the Megalith tour. It’s run by a young archeologist and is my favorite thing to do in Evora.

I'm not sure your routing makes sense. What about saving Lisbon/Sintra for the end of your trip? Upon arrival, take the train to Evora. Pick up car when leaving Evora, see your sites, make your stops (Alcobaca, Obidos etc), then drop car on way into Porto. Train from Porto to Lisbon when done. You wont' need a car for Lisbon or Sintra.

We really enjoyed the Roman ruins at Conimbriga. We decided to skip Coimbra.

Roads are in good condition and well signed. If you aren't familiar with round abouts, do some reading up! We loved travelling by car and it allowed us to see much more of this beautiful country. People are super friendly and happy to offer assistance with directions.

Enjoy your trip!

Thank you both for your comments. We do have experience with roundabouts both in France and Italy so that doesn't bother us. We know that we will leave the car parked at times. We won't get it until we leave Lisbon. I looked at Coimbra and have mixed feelings about that. I have read so much about Obidos and it sounds like it would be worth the stop. Too many tourists?

Has anyone done a day trip from Porto to the Galacia Spain for the santiago de compostela?

If you are not locked in to Lisbon at the first of your trip I would suggest picking up the car on arrival and driving a loop beginning with Evora or Obidos area. It sounds like you have the ability to add a day or two? I would make an overnight stop each direction traveling to and from Porto to see some of the sights you mention in central Portugal. Save Lisbon for the end and drop car prior. We took a car to Sintra and knew we would just park it. That could be done very first or very last of the trip by car, or as many seem to do as an overnight by train from Lisbon. Do stay at least one night in Sintra.

It’s too far, IMO, to drive to Santiago for a day trip. However, if you can spend a night there, it’s a lovely place to visit. The hilly country side in Galicia reminds me a bit of the lower elevations in Switzerland.

I agree with Kathleen about your routing. Sintra is so close to Lisbon. I would suggest either going there right after your 4 nights in Lisbon, and picking up car after that, you really don't want to drive there. Or you could do Sintra at the end of your trip instead of Lisbon and go to the airport from there.
I liked Obidos, but it was very busy with tourists in the day. We stayed over there on our last night, which was lovely and quiet, and drove to the airport our last morning. I would prioritize 2 nights in Evora over a night in Obidos. From Evora we drove to Estramoz and also Vila Vicosa. If you go to Vila Vicosa check when the english tour is. YOu have to do a tour ( we ended up doing a portuguese one)

Thank you all for your advice. We always have a car when we travel abroad. I understand that we don't want to drive in Lisbon or Porto. When we go to Sintra we are staying in a location that is easy for us to walk to the sites but still have a car in the event we want to venture out to Cascais or somewhere else from there. We are staying in the area for 3 nights. We just want to be able to relax and take our time to enjoy the area and potentially see it as well at night when the tourists all leave. My question regarding Porto is, 1) is it better to stay in the city center? or 2) in the Vila de Gaio area? We will be staying there 3 nights. We plan to tour the Duoro valley one day. We are thinking about take a day trip (via tour) to Galacia, Spain. It doesn't leave us that much time in Porto and so we may opt out of that. Since we will have a car, we are trying to figure out best place to stay where we can just park the car and not worry about it for those 3 days. Also, I am trying to figure out best place to pick up a car when we leave Lisbon. We will be heading up to Porto but hope to make a stop or two along the way. Would we be better off taking the train to the first stop and picking up a car there? When I do a search for hotels with Parking it seems like they are all paid parking at a lot nearby.