A week is not a lot of time.
You will need at least 2 days if not three in Lisbon as you want to cover the following:
Lisbon Centre (The Baixa)
The Alfama & Castelo São Jorge.
Belem (Tram or train) - Tower of Belem, Jeronimos Monastery
Evening - Bairro Alto
Sintra - Train from Rossio Station (Full morning if not more.)
To the South of Lisbon the following places are worth considering:
Alentejo
Evora (UN world Heritage site)
Serpa
Setubal
Algarve
Lagos - where I live! Great town with a great mix of culture, restaurants, beaches, view and coastline exploring out to Sagres at the most South Westerly part of the Algarve.
To do all the above would require a car and a lot of driving. (Bear in mind to specify automatic shift when renting a car - most hire cars here are manual shift.)
In summary, I would suggest:
Day 1 - 3 - Lisbon
Day 4 - Evora
Day 5 & 6 - Lagos & south west coast
Day 7 back to Lisbon.
No disrespect to Cubsur who has extensive knowledge of the Algarve and Portugal, but I will always prefer Lagos over Albufeira! :::))))
