Recommendations of which towns to visit in Central Portugal

Alcobaça should be a priority for your visit. It can be combined with a visit to Batalha too. Add Tomar. Do not waste time on Nazare, a touristy beach town!
Spend a couple of hours on Obidos at most. We made the mistake of staying there. Two hours is enough.

Tomar is well worth it particularly the castle remains and the convent attached to it. The town is great too!

Definitely visit Alcobaca! My most favorite cathedral in all of Europe and I’ve seen many.

It would be easy to visit most of the places you mentioned if you have a car. Fátima, at least the shrine part, can be seen in a couple hours. If you’re not very religious, you could skip it. Tomar is worth a couple days, the monasteries at Alcobaca and Batalha are worth visiting, but with your limited time you may want to select just one.

When you said Leira, did your really mean Leiria? It is closer to the other places you mentioned.

Yes, I meant Leiria, not Leira.

Any recommendations to see this town?

There was a comment about Nazare, and the town was not recommended to visit. Anyone concur?

Thanks!

Leiria Is the one town I haven’t been to, so can’t make a recommendation. I did a quick check and it seems to have the same type things to see as many other towns, churches, a cathedral, parks, etc. it doesn’t seem to have a “must see” sight.

I’ll be in Nazaré next month for a couple days. Some people don’t care for it, but I wouldn’t not visit it based on one person’s opinion. Look it up on TripAdvisor to see what it has to offer and if it might be a place you want to visit. One thing I want to see there is the Miradouro do Suberco. Hopefully some huge waves will be coming in when we’re there. I also want to see the small Chapel of the Miracle's Memory and Sanctuary of Our Lady of Nazareth. How touristy it is will depend on the time of year you visit it. I see it as a place to relax.