Thoughts on Itinerary

Obidos can be covered in a couple of hours and I would prefer to stay in Evora where there is far more to see, rather than Obidos.

You are short changing Lisbon itself, but you will get a taste for city, coast and inland Portugal with your itinerary.

I agree that you are shortchanging Lisbon. And, Obidos would not be my choice for an overnight stay as you can see everything in a couple of hours. With your limited time, I would encourage you to rethink renting a car. Driving in the central part of the country is easy and rates are usually quite good. Pick up the car outside of Lisbon at a smaller town to save the stress of Lisbon driving.
It will be difficult to see Alcobaça, Batalha and Tomar in one day, especially if you don’t drive it. I would pick either Batalha or Alcobaça and not both with your limited time frame.
I like São Martinho do Porto but be aware that the beach is very calm - almost like being on a lake. So if you want to experience of ocean waves, you really won’t get that in São Martinho. And,again with your limited time, you might want to think about beaches closer to Lisbon.
I agree with your plan to skip Porto and Algarve this time.

Hi Andrew, that's interesting, you're the first person I've heard who prefers Porto to Lisbon. What about it did you find superior? Thanks!

We visited Portugal 2 years ago. We felt 3 nights in Lisbon gave us an overview of the city sites and landmarks. We took a wonderful guided day tour to Sintra and surrounding region. Spent one night in Evora which was perfect.

As far as Obidos, it's a nice base for sites heading north, but we felt the 2 nights spent there was "overkill." Lovely place to come for several hours. It's very touristy and crowded when the tour buses arrive. We completed our tour in Porto and the Douro Valley. We loved Porto. We liken it to a "mini" Lisbon.
Bon Dia.

Eight days in Portugal may sound like a lot, but it will fly by. Moving from hotel to hotel eats up a lot of time. My advice would be to make Lisbon your base, and do day trips to Sintra and Evora, and maybe Obidos. Given your interests, there are a lot of things to do in Lisbon. There are more than 100 museums in Lisbon (try an internet search using google and popular travelers websites), great food, fado, and lots of opportunities for cultural encounters. There are good beaches on the west end of Lisbon (Cascais), if that is what you want. As mentioned earlier, a rental car is much more trouble than it is worth in the Lisbon area.
Yes, Porto is also a nice place to visit, but your time is limited.