Looking for some places to staythat are easily accessible to day hikes
Well, there are several Camino routes that go through Portugal, so you might want to look at those to see what cities appeal to you the most and that are easy for you to get to by bus or train, especially to return to after walking all day.
There are a couple of nice, scenic hikes up to schist villages. One is not far from Coimbra and departs from Lousã castle, heading to Talasnal and beyond. Another is a bit more remote, leaving from Piodão and passing through Foz D’Egua. A Google search will get you lots of info on both hikes.