There is a lot of choice regarding staying in Lisbon with children, for every budget there is a different option. If you stay in Lisbon for a short while, like 3-4 days, then we advise you to look for accommodation in the city centre (or nearby). If you stay in Lisbon for a longer period of time, why not rent something outside Lisbon, such as in Cascais or Sintra. The train connection between Cascais and Lisbon is good and it takes about 30 to 45 minutes to the city center. If you rent a car then Sintra (and surroundings) is a great option.
Accommodations in Lisbon
If you’re staying in Lisbon with children we advise you to find accommodation just outside the city centre. Think about neighbourhoods like Estrela, Príncipe Real and Campo de Ourique. These districts are within walking distance of the centre but often have more space, a variety of child-friendly parks and good connections to the center. A good startign point is to look at Bed & Breakfasts in one of these districts.
Accommodations outside Lisbon
If you choose to stay outside the city with your family, think about what you want to have around. If you opt for a beach within walking distance, then Cascais or one of the suburbs of Lisbon such as Oeiras (https://www.booking.com/bed-and-breakfast/city/pt/oeiras.en-gb.html?aid=1167364) or Carcavelos (https://www.booking.com/bed-and-breakfast/city/pt/carcavelos.en-gb.html?aid=1167364) are a smart choice. All these places are also easy to reach by train.
If you’d rather have some adventure and nature, then Sintra (https://www.booking.com/bed-and-breakfast/city/pt/sintra.en-gb.html?aid=1167364) or Colares (https://www.booking.com/bed-and-breakfast/city/pt/colares.en-gb.html?aid=1167364) are your best bet to look for an accommodation. Nature here is more rugged and you have some very nice castles and exciting quintas in the around!