Enjoy walking in towns/cities that may be picturesque, have "old town, historic sites, well preserved buildings, possible walks along rivers, lakes.
I think one of our favorites is Elvas. It is a marvelous walled city on the Spanish border. There is easy to find public parking under the Praca do Comercio. From there, you can walk to the castle and perhaps, stop at Igreja de Nossa Senhora da Consalacao to walk on the roof and see Spain before you. It is a short drive to Forte de Nossa Senhora da Graca which is an historic star shaped fortress. There is also an aqueduct that you can walk along.
We loved our day trip so much that we returned in November of 2021 for three days. I could have stayed longer and will most likely return on our next trip to the Alentejo. So many other great places in the Alentejo that we have stayed in.
As you want to travel via Monsarraz ,take alook at Moura and Lake Alqueva(man made lake).It would be on your route with a small detour.