Portugal 2-week honeymoon

My husband and I are planning a September honeymoon to Portugal. Roughly 13 days not including travel. We’re thinking a combination of Lisbon, Porto, Algarve region, and Azores (Sao Miguel Island).

Are we trying to fit in too much in a 2-week trip? If so, we would love advice on which stop to eliminate. I’m pretty torn. My husband is thinking maybe eliminating Porto if we had to choose.

Are there any areas where we would definitely want a rental car? Thinking we would fly into faro and rent one while we’re down in the algarve region then drop it off when we get to Lisbon.

Any must-do’s or general recommendations are greatly appreciated!