We visited the Algarve, but it is a fairly long drive for only 1 or 2 days, and definitely too long for a day trip. Are you just looking at day trips or staying overnight before going on to Lisbon?
If this is day trips, there are a lot of nice small towns in the Alentejo that I would consider. We saw Vila Vicosa and Estremoz, and I believe Elvas is also a UNESCO site and only an hour away. And there are many more towns south of Evora as well. If you drive into Spain, you may need to get a different transponder if you will be on any toll roads. There are also a number of wineries in the Alentejo region that could be worth a visit, if you enjoy wine.