We are planning to go next June and will not be renting a car.
What is the best order for this plan-open to taxi, uber, bus, train but would like ot avoid multiple transfers if possible. Tentative plan- Nazare- one night or day trip, Obidos- 2 nights, Porto 2 nights.

Are you planning to fly into Porto or Lisbon? Obidos is pretty much a day trip from Lisbon, not sure why you would need to spend two nights there, in my opinion.

We stayed at the pousada in Obidos, liked the pousada but were done with everything in Obidos in a couple of hours.
Instead of Nazare, visit Alcobaça.

Nazaré is a summer resort town along the waterfront with an old town behind it. For the five nights that you have allocated to this trip I do not think that it is worthwhile. Alcobaça is a better choice. We liked Nazaré, but we had more time to spend for secondary sights.

Many thanks to all those who provided suggestions. They are noted!
However, I have been to all these places many years ago and I am seeking advice about the mechanics of travelling from one to the other. Any suggestions about that issue are most welcome.

I take trains where possible and buses where not. Info on trains in Portugal - https://www.seat61.com/Portugal.htm

Entirely agree that Obidos is a day trip, not two nights. Friends of mine insisted on one night and said afterwards that it was a mistake. Are you doing a loop from Porto or does this trip include Lisbon? If it has been "many years" since you were there I think you will be surprised by how popular Portugal has become.

Thank you.
I want to go to Nazare for the day to see the enormous surf "in person". Have watched a lot of surfing videos and would like to see this for myself.
We are wanting a kind of slow travel. Staying in a place, visiting the markets, walking, meandering, having a glass of wine - not tours/typical sightseeing.,
Welcome further advice re Uber/taxis- can one use this to go - for ex- Obidos to Nazare?

Just Google the two end points of your destination and then click on your mode of transportation to get an answer. For example: type Obidos to Nazaré by bus and you will get this answer:

https://www.google.com/search?client...ih=545&dpr=1.5

Are you sure that you'll be in Nazaré just at the right time to catch the big waves? It can be very hit or miss.
https://nazarewaves.com.

Unfortunately this area of the coast is not conducive to train travel.

Check the schedules of the Rede-Expressos,, the national bus carrier to see the Lisboa-Nazaré bus schedule. It has an English page.
RT | Rodoviária do Tejo
You'll see that there is a direct bus, for example, departing from the Lisbon Sete Rios station to Nazaré. It takes 1 hr. 45 min.

From Nazaré to Obidos, there are only 3 buses a day at 6:25, 7:30 and .17:10 See the schedule here-
RT | Rodoviária do Tejo
The bus takes about an hour.

From Obidos to Porto, you may have to take a Rodo Tejo, Rapida Verde bus to Caldas da Rainha, and from there, f rom Caldas da Rainha another direct bus or.... not as convenient, two trains up to Porto. The quickest bus, Obidos to Porto, takes 3 hrs. 15 min.
Again,
www.rede-expressos.pt
www.cp.pt

As thursdaysd has mentioned, if you haven't been to Obidos for many years, you may find it very changed and now very heavily touristed, especially by bus tour groups during the day.

The monastery at Alcobaca is awesome. We were there midweek in the morning and had it practically to ourselves as compared to the monastery in Lisbon where people were online for hours in the hot sun. We never stopped at Nazare heading north to Porto but we did really enjoy our stop in Aviero and took a refreshing canal boat ride after coming from very hot Coimbra, university impressive to see along with the historic churches if you've never been there.

My cousin along with two adult daughters were in Portugal during February school vacation and were two nights in Lisbon, two nights in Sintra and two nights in Cascais and traveled the entire time by Uber.

Thank you to all for the helpful suggestions!

Just a correction of my post above-
The Rede-Expressos operates the Lisboa Sete Rios to Nazaré bus.

The page for the Nazaré to Obidos local bus is
RT | Rodoviária do Tejo

Maribel posted a good link for the waves. We did not see anything akin to a big wave at the end of May, although the coast is always pretty. But if you’re going for waves, think winter season.

Yes, absolutely think of winter season! Last year, I believe it was in January. The big waves happen mostly in the winter and are tide and wind direction dependent, so unpredictable.