If you go to Lisbon some things to see are:
Castelo de Sao Jorge - big castle on top of one of the hills
Torre de Belem - Another little castle on the river front
Mosteiro dos Jeronimos - great big church, worth a see if you aren't sick of europes churches by then.
Cristo Rei - a big statue of Jesus across the river from the main city
If you go out at night go to Bairro Alto, it is where all the students hang out and you can find all sorts of cool bars and clubs there (don't get too drunk the streets all look the same)
If you mean where to travel outside of Lisboa. Other cities/areas to see are Sintra, Cascais or Sines. All great places worth a visit (at most 2 hours drive away) over 9 years ago
Day trips from Lisbon I would say:
-Heading North (max 2 hours)
Cascais, Guincho, Sintra, Mafra, Ericeira, Óbidos...
-Heading South (max 2 hours)
The coast (last beaches in Costa da Caparica, Praia(beach) do Meco, Portinho da Arrábida, Tróia, Comporta, Santo André, Sines... about 9 years ago