Another case of "If its Tuesday, this must Belgium!"
1) You are on holiday so relax! Don't try to fight the jet lag.
2) If you are flying TAP or assocate airline in the Star Alliance combine, I would fly into Lisbon and straight away get the connector flight to either Porto or Faro airports. It should not cost much more I would of thought and will save a lot of agro.
3) If Porto, check into your hotel and have a kip. Then relax that night on the old river front having a drink and a dinner.
4) A couple of days later take the train down to Lisbon and spend 4 days there.
5) Then come down to the Algarve, (I would recommend Lagos or Tavira). You only need a couple of days here and will only really be able to visit one centre based on your limited schedule.
6) Fly back from Faro Airport to Lisbon on the TAP connector and back to the other side of the pond.
