I have been there with him, too. It‘s Pastelaria Paço Real, Rua da Conceição.
It’s near the intersection of Conceição and Rua da Prata. They have a very nice stamp with a peacock (which is the name of their pastelaria in Portuguese). It’s definitely a “hole in the wall” kind of place, with excellent pastries and good home cooking. I’ve been back with my husband on non-walking trips several times.
It is also around the corner from a family run, clean, basic, pensao called Pensao da Prata. It is a great central location for touring Lisbon, and about a 12 minute walk from the cathedral and the Santiago Church, where you will start to walk if you start in Lisbon.
Heads up on the pasteis de nata — the Pastelaria de Belém is the only place I know of where they are served hot. There is a big debate about whether these should be served hot or cold, so you will get the chance to enter that debate if you try some in-town places.
For a earlier forum chat on this topic, see
this thread.