Sintra, Lisbon, Coimbra, Porto - What not to miss?

We stayed in touristy Obidos, a mistake. It is good for a few hours at most. Cute village full of tourists! We stayed in the Pousada there. Parking was difficult.
Coimbra- the university’s historic library is a must see, the most important site there. . Conimbriga is a Roman archeological site outside of the city as you approach it.
We drove to Evora from Lisbon. No tour needed, just use your guide book. You can also take a bus I believe. When at Alcobaça, find the royal tombs, especially King Pedro and his Inés. Look up their story as it took place in Coimbra. We thought Alcobaça was beautiful in it’s simplicity.
We had lunch in Aviero one day, walked around awhile. Worth a stop.
We enjoyed both Lisbon and Porto. Be ready for hills in Lisbon, like San Francisco.
Belem was a favorite part of Lisbon for us. In addition to Jeronimos Monastery do not miss the Coach Museum there.
And eat as many pasteis de nata as you can! Yum.
To clarify, we also always rent cars and rarely take a tour.. Portugal is a very easy country to navigate independently. We prefer being more in control of where we go and how much time we spend there, the flexibility. We loved Portugal!

For your day 3 look at Batalha monestary instead of or in addition to Alcobaca. It’s a debate but I preferred Batalha, others prefer Alcobaca. Look at pictures of and articles about both, see if you can do both or if you prefer one over the other. We did both on a driving day trip from Lisbon with a very short stop in Nazare, mainly to see some waves. Did not get to Obidos.

Day 5 is a lot to accomplish in one day. On paper, it looks like departing from and returning to Coimbra, Bussaco and the schist villages are possible, but I think that managing both of these in the same day would be challenging. The roads in/out of the area of the schist villages are narrow, winding, and time consuming. If you're going to make the effort to get there, spending some time would be in order. Have you looked at visitportugal.com? It has some good info on the villages. As for Bussaco, how much time you spend there depends on what you want to do -- walk in the forest for a bit, have lunch at the pousada or a bit of both? I guess what I'm saying is don't underestimate the driving time and/or time needed to appreciate each site. (My experience with google maps is allow at least 1.5 times the time it says you will need.) You may find picking one or the other is your best option.

It all depends on your interests. What do you like to see and do? We spent 5 nights in Lisbon that included a daytrip to Sintra. So I can't comment on the other places.

For Lisbon, this is what we loved:
Gulbenkian Museum
Sao Jorge Castle - after we visited the castle, we slowly wandered around the Alfama district. This was one of our favorite days. We sort of followed Rick's walking tour.
Mosteiro De Sao Vicente De Fora - we saw this the same day we were in the Alfama. Beautiful blue and white tiles. Awesome views from its rooftop terrace.
Belem - Jeronimos Monastery, Discoveries Monument (we took an elevator to the top for spectacular views. There were no lines!)
We saw Belem Tower from afar but did not wait in the long lines to go to the top.
Coach Museum in Belem
Sao Roque Church
Stop at miradouros (viewpoints) for gorgeous views and drinks.
Time Out Market
Dinner at Cervejaria Ramiro for delicious fresh fish and shellfish.