Located near the access road up to the Castelo de Sao Jorge is one of the prettiest lookout points of Lisbon: the Miradouro de Santa Luzia. From here, you can oversee the Tagus and the terracotta rooftops of the Alfama district. Of course, knowing you, you'll probably be more interested in the local cat.
Cat pictures by Claudia Mannes
P.S. More cats of Lisbon.