Portugal Honeymoon Advice

We’re planning a honeymoon in Portugal this June, flying roundtrip JFK – Lisbon (arriving 8am on Saturday, departing 10am the following Monday, totaling 9 nights). We want to visit Lisbon, Sintra, Cascais, Porto, Douro Valley, and the Algarve.

I’m considering 3 nights in each location, but I’m torn on the order.

Options I'm considering are:

– 2 nights in Lisbon, then head to Porto for 3 nights, down to Algarve for 3 nights, then one final night in Lisbon before the flight

– 3 nights in Lisbon, 3 in Porto, 3 in Algarve, early morning on departure day

– 3 nights in Porto, 3 nights in Algarve, end with 3 nights in Lisbon

– Go right to Porto first and do 3 nights in Porto, 3 nights in Lisbon, 3 nights in Algarve to break up the travel time?

My other question is this – is it worth doing 1 night in the Douro Valley, so 2 nights in Porto and 1 in Douro Valley, or do we just do a day trip from Porto?

Also, suggestions on flying vs. train vs. renting a car to get around?

Thanks all!!