1) The Alentejo between the Algarve and Lisbon is lovely but probably not exactly interesting to easily bored teenagers.
2) Bear in mind that, on the motorway, one can drive from Faro to Lisbon in under 3 hours.
3) If you are interested in history, a route from Faro via Castro Marim, Alcoutim, Mertola, Beja, Serpa, Alqueva (Dam), Reguengos de Monsaraz, Evora, Setubal/Palmela would be interesting.
Bear in mind, however, that the temperatures in the Alentejo will now start to climb and will be, during the day, between 35º and 40ºC for the next 3 months. I personally do not recommend this interior region for touring without an air-conditioned car during this period.
Another option is to run along the Algarve Coast via Lagos, (divert to Sagres), and then up the Coast via Vila de Bispo, Carrapateira, Aljezur, Rogil, Odeceixe, Vila Nova Milfontes, Sines and then Troia. Take the ferry acoss the Sado at Troia and then Setubal/Palmela and Lisbon. Not so much history but cooler and lots of beaches.
