You have several choices:
You currently have subway from the airport which will make life easier. But still, depending on the time you arrive to Lisbon and how old the kids are I would or not risk go downtown. The subway can be very crowded at rush hour.
If you have a stroller I would only consider it if it's not rush hour. People are kind and will almost for sure help, but it can be painful and you have to change at least once.
Go to "Parque das Nações". It's not a historically iconic part of the city but it's 3 subway stations away from the airport. It´s a new and nice area, built specially for Expo 98, with lot's of gardens, Ocenario, a cable car, several restaurants, near to Tagus river. You can either walk a bit, use the cable car and enjoy the scenary or just relax in one of the gardens or a cafe.
You can go to "Parque das Nações" and visit Ocenário (photos). It's worth it and kids love it. (Ocenário is the biggest aquarium in Europe and the second in the World).
Go downtown (Option 1). It's a bit more tricky. You have change once between subway lines and it will take you aprox 30 min. You can get out in Rossio and walk to Terreiro do Paço. There you will be able to see the castle (in the Hill), see Lisbon architecture and urbanism (this area was built by Marques de Pombal, after the 1775 earthquake).
Go dowtown (option 2). Get out in Rossio and find "Calçada da Gloria" You get the tram here and go up the hill. When you arrive you will be near "Bairro Alto" one of the typical neighbourhoods of Lisbon and "Miradouro de S. Pedro de Alcantara" with a great view over Lisbon and to the Castle.
Go downtown (option 3). Instead of going to to Rossio go do "Marquês" by subway (again, it will take you aprox 30 min. to arrive). From there you can walk down "Avenida da Liberdade" to Rossio. If you look back when starting, you will see the beautifull "Parque Eduardo VII". Avenida da Liberdade is considered one of the most luxurious avenues in the world. When arriving to Rossio don't forget to drink the :) world famous "Ginginha". Near by you can find "Casa do Alentejo", currently an association and a restaurant. Before a Palace. You can go in a see the architecture. It's a very beautifull and unexpected place (nice for a quick visit).
If you just want to relax a bit and get away from the aiport you can do it also in "Alameda D. Afonso Henriques". It's easy to arrive by subway and you can do a bit of tourism sitted in a garden bench. It has a playground with swings for kids. It's not an amazing "must visit" area. It's just nice to relax for a while and it has its part of history. Alameda was built during "estado novo" when there was a dictatorship in Portugal. In one side you can see "fonte luminosa" an imponent fountain (recently repaired). In the other side there is "Técnico" one of the best portuguese universities. There is also a Theater in the middle called "Império" (Empire - iconic name, like the architecture of the fountain, to show Portugal a great country - regime propaganda). Currently "Imperio" is a church from "Igreja Universal do Reino de Deus". These are all built with the same kind of architecture.
(Note: if you want to eat, I would advise you to visit "Cervejaria Imperio" under the Theater. It used to have one of the best stakes of Lisbon. It's not what it used to be but it's still a very nice place to go and not expensive if you have the buffet lunch.)
Another alternative may be going to "Quinta pedagogica dos Olivais" It's a small farm in the city with several farm animals (horses, donkeys, sheep, chickens, etc) specially made for kids. They often have activities like baking bread, etc. (but you have to enroll for these). It's a nice place, it's free (you can just walk in) and it's near the airport (you can get there by subway also, it's 4 stations away from the airport). It's usually open from 10h to 19h except monday (closed).
- Here's a map of the Lisbon subway system. You can easily find the metioned stations above. For a quick reference:
- Aeroporto in the red line is the airport station.
- Baixa-chiado or Rossio gives you direct access down-town.
- Terreiro do Passo also leaves you downtown and near the river.