Portugal itinerary 52 days by public transportation

The order of towns looks pretty good to me. But, my first thought is you have way too many moves. A number of towns could be done by day trips and save you the hassle and time of checking in and out of hotels so much.
After Coimbra on your list through Peniche - all could be done by day trips. But, yes, you would need to rent a car. However, driving in the silver coast area is easy. And, buses to some of these cities would take many hours.

Buses in the Algarve region are the same. Buses are infrequent and driving is easy. You could stay in Tavira and Lagos to give yourself home bases to visit the other towns.

The two main bus companies are Flixbus and Gypsy. Gypsy is spelled a bit different but if you type in the regular spelling it will come up.

100% agree with kathrynj. Try not to make so many moves as there is no real need to if you are able to anchor your stay in several anchor locations and then make day trips. You might find the rome2rio app helpful regarding public transport.

Agree too. We’ll be visiting Portugal in October 2024 and are just staying in 3 cities with day trips. We’ll be basing in Porto, Tomar, and Lisbon. We will rent a car leaving Porto and drop off when we arrive in Lisbon.
Checking Rome2rio driving times to Fatima, Obidos, Coimbra, and a few other places are all around 1 hour from our Tomar base.
We really hate packing up and moving too many times and we never stay less than 3 nights. Our trip will be 16 days.
Good luck with planning.

I was in Portugal last October.

Lisbon has wonderful public transit and I think that you can get a transit card for several days that gives you unlimited access to public transit.

I took the train from Lisbon to Sintra. Very easy. And once in Sintra, there is public transport to take you to the top if you so desire. However you can walk to the top as well.

I do not think you need to overnight in Sintra. It probably will not be terribly crowded February through April and it is easy enough to get there from Lisbon.

In Lisbon, I took a tram to Belem which is highly recommended.

Lisbon is a wonderful city. Are you wanting suggestions for a hotel in Lisbon.

I took the train from Lisbon to the airport. You will be needing to take the red line. Depending on where you are staying, you might have to transfer from another line to the red line but it is all easy enough.

I was on a shore excursion in Braga and will only offer that it is fantastic.. f you want any suggestions of places to go, just let me know

By reading your discussion, I am thinking you are only asking about public transportation.

I'd recommend picking up a car when leaving Porto and then dropping it off prior to your stay in Lisbon. The Minho and Silver Coast are most ideal by car. You could base yourself in one location in the Minho region and day trip to Braga, Guimaraes and a few other towns that are wonderful (Ponte de Lima, Viana do Castelo, etc.) And then have another base on the Silver Coast and day trip from that base. Personally, I wouldn't plan on seeing all of those sites and being stuck moving bases that frequently and dependent on the buses.

Even my most recent trip to Portugal was so long ago the details are no longer with me, but I remember liking Viseu.

I agree with others that you need to consolidate a lot of those 2-night stops into bases from which you can take short day trips by train or bus. In addition to making the trip feel less hectic because you won't be packing and unpacking every second day, longer stays in fewer cities give you built-in flexibility. You can look at the weather every morning and choose whether to head somewhere with mostly indoor or mostly outdoor sights.

I find rome2rio extremely unreliable as to travel times, frequencies and fares. It's not even 100% accurate about whether bus service exists from one city to another, though it's pretty accurate there. You need to go to the websites of the rail company or the bus company to find out what's really available. For areas where you might drive around, I'd use ViaMichelin.com for routing suggestions and driving times, but understand that the latter do not include stops, traffic delays, looking for parking or walking from your parking place to the sights you want to see.

You obviously enjoy travelling at a very fast pace. Exhausting trip. I know the Algarve well, and agree with kathrynj, base yourself in maybe just Tavira and Lagos.  Moving to Albufeira and Faro for 2 nights /1day is hardly worth it. Tavira is one of the prettier villages and Lagos is a decent size for a base.  

Driving is easy in The Algarve, but I note you require public transport. Taxis are a consideration and well priced.  There are larger bus stations in Portimao and Faro. I could be wrong here, but I note on the Alsa site (see below) for example there's a bus from Portimao to Tavira (via Albufeira and Faro).I have travelled many times by Alsa buses between Seville and Portimao/Faro. But not internally. There are trains from Lisbon to Faro or Portimao.

ALSA
https://www.alsa.com/en/web/bus/internacional/portugal