No car...suggestions needed

You don't state your interests, which would be helpful for giving specific advice.
Public transportation in Lisbon, Evora and Porto is quite good. With a base in those cities, it is easy to make day trips to a number of other interesting places. Nazare is a beach resort town. Coimbra is a good sized city with one of the oldest universities in Europe.

Tomar is worth considering. It is an interesting town very accessible by train from Lisbon or Coimbra or Porto but much smaller than those three. The Knights Templar convento is a Unesco World Heritage site, major attraction, quite fascinating, but had relatively few other tourists compared to popular sites in Lisbon and Porto when I visited in June.

Why Salema?
Seems difficult without a car
Long train/bus ride from Lisbon and to Évora
You lose good part of 2 days in transit

Another vote against Salema unless you have a car. There aren’t any trains and the bus service is sketchy. Stay in Lagos or Tavira if you must visit the Algarve, although with only 14 days, I would exclude the Algarve and focus on the more interesting area between Lisbon and Porto, otherwise you are going to spend too long in transit.

I am also not a Nazaré fan but the towns of Tomar, Alcobaca, Coimbra and Batalha are all worth a visit. Your trip would be enhanced by hiring a car.

I encourage you to look outside the RS "box". I used his guide book, Lonely Planet, Moon, and Frommers along with the other sites I mentioned in your other post to plan our 24 night trip.

Just to name a few places Rick doesn't mention at all- Tomar, Aveiro, Guimaraes and Braga
If you want a "water" location- Aveiro might fit your itinerary- not on the actual beach but looks charming for a 1 or 2 night stay, easily done by train from Coimbra, Lisbon or Porto.

There is a great trip report written by Priscilla- - her trip was all done with public transportation- lots of good info, there are 4 segments- just follow the links thru to all of them
https://community.ricksteves.com/travel-forum/trip-reports/portugal-our-trip-in-progress

Here is another with lots of interesting suggestions:
https://www.atlasobscura.com/things-to-do/portugal/places

Sintra is much better as a 2N stay than a daytrip with all the hordes. Easiest way to get there with luggage is to take Uber, not expensive and about 35-40 minute drive, door-to-door from central Lisbon (barring traffic issues) or from the airport. Consider going there on arrival, then spending time in Lisbon. I know nothing about Salema. I spent 2N in Coimbra for 1 full day and loved it (arriving late afternoon, leaving in the morning). From Coimbra I went to Aveiro for 1N, and took an afternoon train to Porto. Glad I did.

I had a car in Tomar, which I used as a base for sights harder to get to. I was much less impressed with Tomar as a destination than Coimbra. Unlike many here, I was less impressed by Evora. If the megaliths (I skipped them) are a priority, then you'll want 2N there. Both Evora and Tomar are kind of outliers by train. Look at schedules on the official train site.