3 one night stays vs longer in one?

Either using public transportation or renting a car, I don't think your plan is good. I had 2 nights in Coimbra, arriving late afternoon and leaving in the morning, and I happily filled one full day, which was enough. Coimbra is an easy train trip from Porto. After that, not at all fast or easy. There's a lot of driving, and difficult parking in Obidos and much of Evora. Getting from Obidos to Evora is another slog. You'll be using up much precious sightseeing time just getting from place to place.

There are day tours from Lisbon to Obidos if that is a must-visit for you. What I most enjoyed about Evora was spending a half day a few kilometers outside the city (I had a car) at a cork farm. Most folks on the Forum seem to have liked Evora much more than I did. A day trip by train from Lisbon might be feasible (check the train schedules). The trains are much faster than driving, certainly more than buses.

As I reread your post, you say 10 days in Portugal, but then you count 10 nights. If you indeed have 10N (11 days), I'd spend 1 or 2 in Coimbra and take the train to Lisbon. I'd probably opt for day trips from there, but I don't like one-nighters or schlepping luggage around.

I would never do three one night stays, if at all possible. Coimbra is an easy stop on the train. Leave Porto early and stop for one night. Évora is a one hour ride from Lisbon and deserves two nights so you can go a bit out of town to see the megaliths and dolmans.
Obidos can be seen in a couple of hours and only feasible if you have a car, IMO.

As already stated, Óbidos can be seen in a couple hours. A full day in Coimbra, meaning two nights was sufficient for Coimbra. On our trip we had a rental car,

Agree about Obidos. Even walkimg at a snail’s pace, half a day is enough.