Here my personal tips for some special local activities:
... a gentle trip with the tram to the beach: After renovation work, the historical Sintra Tram has come back to the beach, resuming its original route between Vila de Sintra and Praia das Maçãs, thereby connecting the Mountain to the Sea. The train stop is located 2 minutes from Casa José Ricardo; trips are frequent during summer (from 17 June), at other times of the year our tram operates on weekends only. Timetable.

... a guided botanical walk in the Sintra mountains with renowned Portuguese specialist in the field of medicinal and aromatic herbs and book author Fernanda Botelho. Fernanda studied medicinal plants at the Scottish School of Herbal Medicine in London, where she worked several years, acquiring her knowledge in organic and sustainable farming. Back in Portugal, she develops and organises trainings and workshops about medicinal herbs and has installed gardens of medicinal plants in the parks and gardens of Sintra, including Monserrate, Parque da Pena and Capuchos. Combining a walk in these beautiful gardens with learning about the medicinal properties of the local plants is a rich and stimulating experience!

... Wellbeing, Spa rituals and beauty treatments. Spoil yourself in the luxury environment of Six Senses Spa in Penha Longa, which offers a wide range of holistic wellness, rejuvenation and beauty treatments for ‘Balancing Senses”, administered under the guidance of expert therapists.

... enrich yourself by practicing yoga in the Sintra mountains or on the beach and by doing yoga with the whole family - at the Yoga-Center Centro do Yoga Sintra/Chakra;

... to get to know and enjoy Sintra and its marvellous nature on foot, you can also join the experienced tour- and trekking-guide Filipe Carmo Passos on his Nature Walks in Sintra - Filips'e walks feature exciting night walks as well as leisurely Saturday morning strolls;

... and treat yourself to a delicious meal in the peaceful surroundings of 'Soul Food' - a vegan/vegetarian restaurant, run by an enthousiastic young team of chefs;

Nearby you can
... enjoy one of the most beautiful views of beaches and the relaxing atmosphere in the gardens of Moinho Dom Quixote, a bar/restaurant in a restored windmill near Cabo da Roca;
... watching an open-air theatre performance in the gardens of Quinta da Regaleira (June to September);
... surfing at our local beaches -- check the current wave conditions at Praia do Guincho  or Praia Grande;

My suggestions for a day in Cascais: You could visit the Paula Rego museum and the Farol museum (both very stylish) and spend some time at the beach. If you like to shop for gifts, look for a sweet place called the 'House of Wonders' which is also a cafe and is near the Miscordia church. It has a lovely roof terrace and delicious cakes and salads - perfect for chilling out after the beach. There is now a craft and food market at the Mercado Municipal in Cascais on Sunday - small but well worth a visit. For local souvenirs, the covered stalls at Boca do Inferno (on the seafront, in the direction of Guincho beach), where you can buy various local handmade crafts, incuding ceramic plates and knitted ponchos at very reasonable prices.

A bit further away... Dolphin watching in the Sado estuary: Tour operator Vertigem Azul is offering tourists the chance of a close-up view of the rare bottlenose dolphins in the Sado estuary, south of Lisbon. Guided boat tours along the picturesque Arrábida coast and into the estuary operate throughout the year, with snorkeling stopovers included during the summer months.