To the West of Lisbon city centre along the Cascais/Estoril mainline rail route there's a choice of pretty beach based resorts along the Estoril Coast. One of the first you'll reach, to the West of the historic Belem district is pretty Estoril coast village Paco de Arcos.
Paco de Arcos actually has some historical significance pertaining to Portugal's Age of Discovery! Apparently, King D.Manuel I of Portugal is supposed to have watched Vasco da Gama's caravel ships depart to India from this spot. Paco de Arcos is a superb quiet beach bay choice, offering the benefit of a peaceful beach bay with easy access into Lisbon city centre and Belem. You're also near the Estadio Nacional (home to Portuguese National Football) here for sports events.
Paco de Arcos, alongside nearby Carcavelos make a good half way house base, between Estoril and Lisbon city centre.
Push upwards to to historic Queluz with its palace, and of course numerous golf courses around Lisbon and Estoril. The Queluz National Palace, former sumer la de da residence of the Portuguese Monarchy (with very nice barroque gardens) is open from 10am to 5pm (gardens close 4pm). Closed Tuesdays.
Just up from Paco de Arcos on the coast is the Oeiras district. Here you'll find the Marques de Pombal Palace and Estate, which dates from the 18th Century.
Built by Hungarian architect Carlos Mardel for Pombal, Chief Minister to Dom Jose I at the time of the 1755 Lisbon Earthquake (see Lisbon Earthquake pages on this website).
Well worth a look this palace, it's celebrated for its gardens, but also give you an insight into this rather celebrated figure within Portuguese history - his contribution to the reconstruction of Lisbon post earthquake is legendary. Pombal however remains detested by old Portuguese colonies such as Brazil where he is overall perceived as tyranical.
The Marques de Pombal Palace and Estate in Oeiras is open from 9am to 8pm in summer and 10am to 6pm in Winter. Tel 00351 214 408781. That's for the gardens - for tours of the house you'll need to phone prior to your visit. Other sites nearby include the S.Julio da Barra Fort and the Gunpowder Factory and Museum next to Ribeira de Barcarena which is well worth a look. Tel: 00351 214 381400.