Itinerary Help: Portugal & ??

Hi all,

Currently planning our honeymoon for late August/ Early September 2023. Original plan was to do Portugal for 10-13 nights but looking for advice for the tail end of our trip. Originally planned on doing northern Portugal for 6-8 nights and then going down to Algarve but flights out of Faro to JFK are looking expensive and so is accommodation. We don't want to spend the time back tracking back up Lisbon. Should we go to the Azores instead? Or somewhere in Spain/Italy? I see affordable flights to/ from the Azores and potentially to Barcelona/ Rome/ Sicily. Ideally looking for some beach/sun time.

August 26th: JFK-Porto

August 27-29: Porto (2 nights)

August 29-31: Douro Valley (2 nights)

August 31-September 2/3: Lisbon (2-3 nights)

September 2/3 – September 7/8: ????

Thanks in advance!

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Edit: Budget for flights/accommodation for the tail end of the tip is 3-4K. Already have inbound flights and northern Portugal hotels that ARE NOT counted in this budget.