We're spending three days in Lisbon for a business meeting in mid-May. Will have another 9 days to see the countryside. If we're not terribly interested in going to the beach, does it make sense to skip the Algarve altogether or would a drive through that region provide interesting & varied architectural and cultural sights along the way? In other words (see Rick's suggested itineraries), go directly from Lisbon to Evora and then follow that northern loop he suggests?
There's a lot more to the Algarve than beaches, though the seaside drives are very picturesque. But there are many small & pretty towns in the Algarve that you can discover.
We loved the Algarve, but if the seaside is not your thing, then you would have to visit some of the quaint interior towns to make it worth your while.
For us the Algave meant wonderful weather, wheras our Northern sojourns (Porto area) meant rain.