My first bit of advice would be to not rush - the beauty of countries like Portugal is best experienced by dallying in the cities and out of the way places.

Personally, I'd hire a car on arrival (presumably at LIS) then depending on the travel time to that point immediately drive to the north and stay a couple of days in Porto exploring the area. Then drive south along the coast back to Lisbon over a couple of days visiting Sintra before you get back into Lisbon. Lisbon is worth 2-3 days before heading south again to spend a day or so pootling along the coast until you hit the lighthouse at Sagres - turn left to follow the Algarve coastline, stay a night or two in one of the resorts for a bit of luxury and comfort then blast back up the motorway to Lisbon for your flight home (about a 2 hour drive)