Do like local people do. Go for a sunset walk in the Praça da Republica. After this you can go inside the castle and enjoy the church of Our Lady of Conception and go dow until the Palace Square. great promenade indeed.
During Fall and Winter you can find these vendors on the street selling hot chesnuts. called "castanhas" in portuguese. Castanhas means " brown colored" in english.
Locasted in LArgo de D. Nuno de Alvares Pereira you have the Church of Our Lady of Conception. On the square you have this sanctuary that can be used to light some candles and pray.