Towards Sesimbra's direction you will find Espichel cape and other beaches :

Espichel's cape

Sesimbra's Beaches

A bit more south you will find Alfarim and Meco beaches :

Alfarim

Alfarim II

Meco

Only fifteen minutes from Lisbon by car you have Costa da Caparica  and Fonte da telha which is full of  nice sandy beaches.

Costa da caparica I

Costa da Caparica II

Costa da caparica 

Aroeira Golf

Fonte da Telha

Very close to Praça do Comércio is Castle of São Jorge and Alfma which is a place known by the Fado and the excellent Sardines to eat. A lit bit further you find Parque das Nações and Oceanarium within it.

São Jorge Castle

Alfama

Parque das nações

Oceanarium

When you are in bairro alto and you walk up towards Principe Real again you will find Parque Eduardo VII. Than if you walk down in a straight line you will find :

• Marquês de Pombal Square
• Restauradores
• Rossio
• Rua Augusta
• Praça do comércio

Parque Eduardo VII

Marquês de Pombal

Restauradores

Rossio

Rua Augusta

Praça do Comércio

Situated in Bairro Alto's down-part it is  Praça Luis de Camões which is a plaza dedicated to Luis de Camões who was a very famous Portuguese Poet. Once you are in this plaza and you have Bairro Alto on your left side, If you keep walking straight on you will arrive at Chiado, where you find lots of quite good stores. however if you walk towards the Tejo river you will arrive to Cais do Sodré which is full of night-.life crowded bars.

Praça Luis de Camões

Chiado

Fernado Pessoa  - a very famous Portuguese Poet

Cais do Sodré - Night-life

Next to Estrela you find Lapa, which is one of the most luxury quarters in Lisbon.

 Lapa hotel is highly recommended.

Very close to Lapa you have Principe Real, just before you arrive to the very famous Bairro Alto.

In this place you find very good restaurants and a lot of  night-life.

Bairro alto

Lapa Hotel

Principe Real Garden