A few years back, I rented a car in Madrid, visited south western Spain and the Algarve on my way to Evora. Previous posters have given you great ideas for destinations in Portugal. From Evora, I drove up the eastern side of the country stopping in the disused hilltop town of Castelo Rodrigo. There’s a wonderful B&B Casa de Cisterna. The owner offers a dusk visit to view the petroglyphs in the Coa National Park. From there it’s an easy drive entering the Duoro valley from the west and driving to Porto. Then it’s a great drive back to Lisbon on which you can easily visit Coimbra, Batahala, Alcobaça, Obidos, Fatima and Sintra. Here’s a Google Map that shows the route I took. (Open this in the Google Maps app. If you just use the link, that portion of the route from Porto to Lisbon is not the one I drove. )
I would recommend taking the train from Lisbon to Sintra rather than driving. I wouldn’t visit the Algarve at that time of year as most of the area has closed shop for the season. When you get a car, make sure you get a Via Verde transponder for electronic tolls. PM me with any questions you might have.