24-day itinerary, first time in Portugal

Chani, I'd really encourage you to rethink the dropping of the car. I know you say is $100 extra, but I think you have that much in train fare that you don't need. I don't know if you can change your rooms for the first bit at all, if you can, and change the car I'd suggest this:
Sintra 2-3 nights( pick up car in Sintra at the Hertz)
Evora ( I would personally do 2 nights in Evora ( you could do just 2 in Sintra)
Elvas
Tomar with your day trips, ( I liked Tomar, but I'm not sure is a 3 night place, but might be ok as home base)
Castelo Rodrigo, Regua and drop car in Porto.

Then train on back to Coimbra and then Lisbon. I would try to add extra time in Lisbon, and do your day trip to Cascais then.

If you really can't change your rental car, I'd consider the following:
Train first to Porto. Day trip by bus to Guimares and boat to the Douro
Train to Coimbra
Train to Lisbon

then pick up car for the remainder of the trip until you return to Lisbon and/or Sintra at the end

Either way, it is a lovely country, have a great trip

Given your preference for slow travel, I think you may be somewhat short-changing Lisbon. Then again, it will be relatively easy for you to fly back there to spend more time in the city if it really appeals to you and hit some additional regional towns.

A few thoughts.
First, I’m not certain where you got your information about a $100 drop off fee. I have never had that happen in Europe so just checked. With Auto Europe I found no drop off fee with a second location for drop off. If you haven’t used Auto Europe, I highly recommend them.

Second, IMO Batalha does not need an entire day. 2-3 hours was sufficient when I visited. And, it’s very close to Alcobaça and Nazaré. Doing Alcobaça and Batalha in one day is likely a bit much, but you could easily fit in a beach town with Batalha in one day.

Evora is worth two nights. The Megalith tour outside of town is wonderful and worth an extra night all by itself.

If you have a floater day, I would add it to Lisbon. And, only come to Cascais if the weather is good - which it should be by that time. But, last year the weather was still rainy and cool during that time frame.

Great planning.
We did Evora on a day trip from Lisbon, you can see the town in one full day.
Recommend going up the Douro River Valley. We did a 7 day cruise that was wonderful. If you don't do that, take the train up the valley, the tracks run next to the river on the North side.

For a wonderful B&B stay in the In Patio Guesthouse in Porto. It is the best ever. Only five rooms, so book early.

Cascais, a typical beach resort town. Walk to Estoril from there. Kind of a ho hum experience and we love to be near beaches.
We loved Alcobaça, much preferred it to Batalha. I am very surprised Michelin would tell readers to give Batalha a full day. Find the tombs of King Pedro and his Ines in Alcobaça, read their story first!
Day 12. Obidos would take a maximum of two hours maximum. We had a wonderful seafood lunch overlooking the beach and sea in Nazare and I wouldn't skip it.
Pick up car at airport to drive to Sintra and drop it off Day 17 as you arrive in Porto.
Switch Days18-19 and 15-17. Train back to Lisbon. I cannot imagine not having a car to tour Portugal.

Thanks to you all for taking the time to write. I appreciate all the comments, even if I don't respond to them.

About the car. I checked multiple agencies and decided that Europcar was the best for me because they have more offices and multiple Lisbon city locations. I did some test bookings on Autoeurope and directly with Europcar. Autoeurope doesn't include the city train station locations which are the most convenient for my itinerary. The price seemed to be about the same. There is no specified additional drop-off charge, but when I compare the total price for exactly the same car, same dates, the price is over $100 more with drop off in another city (I tried 3 or 4). Also, the only Europcar location is at the Porto airport. Promo AP train tickets between Lisbon to Porto are between €11-20, considerably less. Based on Lisa's suggestion of Hertz, I checked Autoeurope. The 10-day rental fee is about the same as Europcar, but there's a €110 drop-off fee.

My idea was that if I keep the car for my time in Tomar, I'll be able to visit more places easily. And then it's a relatively short drive back to Lisbon where I'd drop the car and hop on the train to Aveiro. I figure I'll have 2.5 days in Tomar, arriving late after spending time in Guimaraes, and getting to Lisbon in the early afternoon.

Would you add a night to Tomar if there's more to explore by car in the area? Or would you add a night to Regua or maybe somewhere between there and Tomar?

My hotel in Lisbon is so much more than I normally spend that I don't want to use any of my time there to leave the city for day trips. I thought that with 3 nights in Sintra, I'd be able to visit Cascais from there as a day trip.

Evora/Elvas - I had originally planned to spend 3 nights in Elvas, seeing Evora as a day trip. Then I did more research and decided I needed an overnight. I expect to have a good part of the arrival day there (early departure from Sintra, pick up car in Lisbon, drive to Evora) and as much time as I want on the next day before going to Elvas. I had considered visiting the megaliths, but . . . . maybe it's my lack of imagination but I've been to others and they just don't "do it for me." (including Stonehenge and Malta).

Geo - I had looked at In Patio after reading your recommendation (and someone else's) on another thread some weeks ago and it looked great. By the time I figured out my itinerary a few days ago, there were no longer any vacancies. Portugal is getting more popular.

I'm going to post a separate thread for lodging suggestions.