Sesimbra is the closest town (approx. 50,000 inhabitants) at the foothills of the Serra da Arrábida. There you can find shops, restaurants, night life and medical care if required. It also has a beach, which is usually highly frequented, and a fortress with a nice seaview bistro. It hosts several festivals, e.g. in the winter the colourful Carnaval de Sesimbra, in May the Finisterra Arrabida film festival, and in July parts of the Super Bock Super Rock festival.
Apart from swimming and sport fishing services also diving is a popular sport there and there is a famous diving target in the shape of a ship wreck, a Nigerian cargo ship that sunk in 1989.
Setúbal (approx. 118,000 inhabitants) is about 45 minutes away from Azoia, and therefore the nearest large city with shops and hospitals. The ride leads you across the mountain range Serra de Arrábida high above the sea with a wonderful ocean view. The city lies at the northern river bank of the river Sado and also has a wonderful old castle, again with sea view where you can have coffee on a terrace. Other historical building is the Monastério de Jesus from the 1490 which also holds a museum, and the São Julião church with portals in the Manueline style which can only be found in Portugal.
And then, at approx. 60 minutes distance, there is Lisboa (approx. 550,000 inhabitants): The city on the seven hills at the estuary of the river Tejo, the city of the history of the discoveries of new worlds across the oceans, the city of Fernando Pessoa and Luís de Camões, a city with many beautiful places and people to discover. It would be too much to list all the interesting things you can find in any guidebook or on any website; therefore I am adding some links here that provide you with some off-the-track tips like a 1920s-style men-only hairdresser, biking options through the city and sightseeing by helicopter; or coffee places, street artists and surfing; or food places, the famous Ginjinha (cherry schnapps) counter on the Rossio, and finally the Loja das Conservas (a shop where you can buy tins with sardines and tunafish). And here is some information on cultural events.
As Lisbon is easy to reach from Azoia by car it is good for a day trip; there are also buses going from Sesimbra but this takes a bit longer.