Yup, sounds like a raging vacation, right? But in all seriousness, we are interested in recommendations for a convenient and walkable district with nearby places for kids to roam, and ideally good metro connections. There seems to be a number of compelling places to stay -- eager for your input though. Thank you!
I don't have any insights into places to stay, but just wanted to mention the Oceanario - largest aquarium in Europe, ranks right up there with the National Aquarium in Baltimore and the Monterey Bay Aquarium, and it's on a Metro line. Fam will love it.
A few years ago we stayed in a triple room at Residencial Florescente in the Baixa district. It was on a pedestrian only street and close to the Restauradores Plaza and the Rossio Plaza. It was also close to transportation. it was a good choice. Our triple room was a decent size but I have read reviews on Trip Advisor that indicate some rooms can be small but that is true all over Europe. You will not spend much time in your room. Breakfast was included and the price was reasonable. I don't remember taking the metro in Lisbon but I know we did take the tram and the bus. This hotel is in a flat area, easily walkable but Lisbon is hilly. The area around this hotel has lots of restaurants and was very touristy. My kids liked the Belem area attractions and the Castelo de Sao Jorge overlooking the city. We also did a walking tour through the company called Inside Lisbon and we really liked that as our introduction to the city. In addition we did a daytrip tour with them in a small van with a group of 8 to Nazare and Obidos. Pick up was very close to the hotel.
We can second Hotel Residencial Florescente. We have stayed there several times and have always enjoyed it. It is close to all types of transportation and fairly level walking distance to Rua Augusta, and the sea, Elevador Santa Justa, other sights, and several Pracas (squares) where the children can roam. Our grandchildren also enjoyed Castelo Sao Jorge and Tower of Belem, as well as the nearby pastry shops.