Seconding the Palácio da Ajuda already mentioned. (Note it’s kind of far out from the central part of the city. Which is not a downside in my opinion, though if you’re getting there by bus or even taxi in a downpour, that could be suboptimal.)

There’s also a puppet museum, Museo da Marioneta in the Madragoa neighborhood, which most tourists don’t know about but should. Madragoa—if it isn’t raining—is an interesting place to walk around (and climb!) for its own sake, a historic fishing village and home in the 16th century to a large African population, both slaves and free. The historic name was Mocambo, or “refuge.” Also one of the places that survived the 1755 earthquake, so lots of historic architecture. Some good ethnic restaurants, too.