Planning Your Time
You'll want to give yourself a day at least exploring the bairro of Alfama, climbing up to the Castelo de São Jorge (Saint's George's castle) for an overview of the city; another in the monumental downtown area, Baixa, and in the neighboring fancy shopping district of Chiado, and perhaps also in the funkier shops of Bairro Alto. Another again could be spent in historic Belém, with its many museums and monuments. Note that many are closed Monday, and churches often close for a couple of hours at lunchtime. It’s worth noting that Sunday is usually a good day for a cultural outing: many national museums offer free entry until 2 pm every Sunday, while others waive the entrance fee on the first Sunday of each month.
There are other attractions dotted around the modern city, and families will appreciate the child-friendly attractions of the Parque das Nações, the former Expo site. There's easily enough to do and see to fill a week—and it's well worth taking the time to see some of the surrounding area.