Like everyone else, I'd say stay in the Lisbon area. I've been to Lisbon several times, most recently last January for 5 days. And I felt that was just barely enough time to see the 'must sees'.
Lisbon is an incredibly walkable city. It is a joy just to wander around, watching life unfold in its many squares and pedestrian malls. The Portuguese are very welcoming and yet it is clear that they are totally unwilling to become something else just to accommodate tourists. So you get to engage a way of life that is alive, flows at its own pace, has a sense of 'place' about it.
Buy any good guidebook and you'll be invited to explore all sorts of ruins, galleries, museums, neighbourhoods and cathedrals.
I also love Sintra for a day trip. I gather you can also get to Evora and back in a day, although I haven't done that myself. But for history buffs I'm told it is wonderful.
One thing that I've learned from my many years of travel is that when I go to a place, I go to a place. I no longer allow myself to get seduced into side-trips that seem so effortless in the brochure and turn out to be major distractions (if not nightmares) in reality. So save Gibraltar
for another time. Let yourself steep in the mystery, history, culture, food and music of Lisbon.
Lucky you! :)