By car, Elvas is about 3 hours from Lisbon. You will need to cress Tejo, head to Setubal and then follow signs to Evora & Spain (Espanha). Tolls add up to almost E15, which is a lot, but in my opinion are worth the independence from public transport. Roads are incredible, speed limit is about 120 km (80 mph). Gas is VERY expensive.
I rented from Europcar and was very pleased. They have locations at the airport and by Pombal square. I paid $135 for three days with full insurance, and my Renault was fully loaded and drove great. It is surprisingly roomy and comfortable, and the trunk holds two suitcases and two large bags. Prepare to pay a lot more though, If you can't drive a standard.
There is plenty of parking in town, much of it free.
Elvas is quite easy to reach, eithor going from the west or east. From Madrid, Spain take the bus to Badajoz, Extremadura, Spain, and from Badajoz just take a taxi through the border to Elvas. From Lisbon just take the bus to Elvas (or Evora and then to Elvas). The Spanish border city of Badajoz has trains and busses to all different Portuguese destinations.