My husband and I will be visiting for 14 days in September. We'll be in Lisbon for 4 nights, then renting a car & driving to Lagos, staying there for 3 nights. My husband wants to stay in Evora 1 or 2 nights, AND Coimbra for 1-2 nights AND Douro valley overnight, finally in Porto for the remaining nights.. We are generally not fans of hotel-hopping every day, at least i am not! Im thinking of the following itenarary in lieu of all the hotel-hopping:
Lisbon 4 nights
Lagos 3 nights
Evora 3 nights
Porto 4 nights (day trip to Douro valley and/or Coimbra?)
We loved Evora, we originally had 2 nights booked there and added a 3rd. There are some interesting day trips from there as well. I like your itinerary, one possible compromise might be to drop a night from either Evora or Porto and drop your car in Coimbra and stay the night. You could then train to Porto, which has a lovely train station and avoid driving in Porto.
You could drop the Lagos portion of the trip. The Algarve is really the least interesting part of Portugal IMO. There are lovely beaches between Lisbon and Porto, if you must have a beach stay. And, they would be much less crowded. That would give you time to do the other places on your list.
14 nights is not very long. Do you fly home from Porto or do you need another travel day to return to Lisbon to fly home?
(We did 13 nights last September but flew open jaw into Porto and out of the Algarve. September is great time of year to visit Algarve, not high season, cheaper, less crowded, warm but not hot)
We rented a car in Lisbon, drove to Evora for a day visit and then to Lagos for 4 nights. We were happy with the day visit. We could have stayed longer but then we would have had to cut something else out.
Getting from the Algarve to Porto will eat up a lot of valuable time in your current itinerary, about 5 hrs driving or 7 hrs of trains. You can break it up with stays in between, but that will involve more checking in out of hotels and does nothing to change the number of hours you sit in a car or train. You may wish to consider a short and very cheap flight from Faro to Porto. Good luck.