My first thought is that driving on highways after getting off a long-haul night flight is dangerous - to yourself and others. Either spend your first night in Lisbon or take the train and rent a car there. On return, be sure to allow enough time to get to the airport, rush hour traffic around Lisbon can be incredibly slow.
I drove to Evora 1N, then explored the eastern side of the country: Elvas 2N, Castelo Rodrigo 2N, Regua (Douro Valley) 2N, Tomar 3N. It was all wonderful. Evora was my least favorite, though I enjoyed visiting a nearby cork factory. I don't recommend Tomar so much as a destination, but it was a very good base to visit the wonderful monasteries at Alcobaca and Batalha, and Obidos (though if you visit some of the hill towns around Elvas, skip Obidos) and a seaside village (I went to Navare - wasted time). Tomar has an unusual restaurant, Taverna Antiqua where everything is pre-Columbian, the food and drink (very good), the furnishings, the utensils. Castelo Rodrigo was wonderful and I did a nighttime tour of the ancient rock art. Elvas is a pretty walled town with a couple good restaurants, a few interesting sights and it's convenient for day tripping. I spent my nights in Regua at a quinta/winery, they served excellent dinners and really good wines. It's another good place to day trip.
It's definitely possible to visit those places as 1-nighters if you like (I prefer a slower pace) and still see a lot of the villages and other sights. Then you could fit in Coimbra, also well worth a day. I used Carolyn's trip report as a starting point.