Start by being honest with yourself...
We've never been and have about 2 weeks to spend
How many full days will you have once you arrive in Portugal? Do NOT count the day you arrive, nor the day you depart. Most first time travelers lie to themselves about exactly how much time usable they really have there. You may be engaging in the same willful self-deception.
I count up the "days" you have allocated, and they total 13. I'd wager that you actually have less than 13 days actually in Portugal (not including travel days). To have 13 usable days, your trip needs to be at least 15 days long (unless you're popping over to Portugal from Spain or other nearby place).
Next, be realistic about how much time is consumed every time you pick up and move from one location to another (minimum of 1/2 day if you're efficient, more like 3/4 of a day for new travelers). Given this fact, it's generally wise to subtract one day from a first-stab itinerary, so...
3 days Lisbon (day trip to Sintra) - this actually gets you ONE day in Lisbon
2 days Algarve - this actually gets you ONE day there
2 days Evora - this actually gets you ONE day there
2 days Coimbra - this actually gets you ONE day there
2 days Douro River Valley - this actually gets you ONE day there
2 days Porto - this actually gets you ONE day there
2 days Obidos - this actually gets you ONE day there
I think you need to cut your number of stops down - way down.
Assuming your trip is 14 days long, that yields you at most 12 days in Portugal. You have 8 places on your list. That's not realistic for the time you have. With 12 days, I'd limit your itinerary to 3 or 4, certainly no more than 5 locations.