Trip to Portugal in November! Need help with itinerary
 

My friend( 2 women 60 years old) and I are planning a 9 day trip to Portugal. We travel on the high end. We like nice hotels, restaurants, shopping and sightseeing. We are thinking 4 nights in Lisbon at the Lisboa Carmo Hotel. Then to Faro/Algarve for 4 nights and then to Porto for 2 nights.. Is that a good order? Any recommendations for hotels, etc. would be great.