Planning Advice for 15 day trip to Portugal

I would skip the Algarve in favor of extra nights in Lisbon. If you must have beach time, There are lots of beaches closer to Lisbon or along the Silver Coast area. Driving all the way to the Algarve will add a lot of driving and time. You can also do easy day trips out of Lisbon to Sintra, etc. I try to limit the number of times I change rentals/apartments because moving takes up so much of an entire day. Don't rent the car while in Lisbon. Driving and parking are not fun endeavors there.
May will be pretty busy, especially in Lisbon and Sintra.

There is an archeologist run tour of the megaliths outside of Evora that is amazing. Definitely worth an afternoon of your time.
Also, be aware that the Pope is visiting Fatima in mid-May. Unless you want to deal with the crowds, you might want to research the exact days and stay far away from Fatima at that time.

Great advice. Thank you. I've reworked our trip to:

4 nights in Lisbon

2 nights in Evora

2 nights in Obidos

2 nights in Coimbra

5 nights in Porto/Douro Valley

Scrapping the Algarve is the right decision. Obidos is one of the most touristy places I have visited in Portugal. Whilst it is worth a couple of hours looking round the old walls, I would stay nearby in Foz do Arelha if you want to be on the coast or Caldas da Rainha if you want something slightly inland and more traditional.

I agree with Jennifer. While Óbidos is a nice place to visit, it doesn't deserve two nights. I stayed in a small town - São Martinho do Porto for a week and did day trips to Óbidos, Alcobaça, Batalha, Foz, and Nazaré. A small town that is central to the places on the Silver Coast you want to visit is better IMO than Óbidos. Other than that small change, your new itinerary looks good.

Thank you all for your advice and recommendations. It's been very helpful. I think I've finalized our itinerary. I can't wait and I think this will give us an excellent flavor for the country and people.

4 nights Lisbon

2 nights Evora

2 nights in Foz do Arelha or São Martinho do Porto depending on sleeping accommodations

2 nights in Coimbra

5 nights in Porto

I would go to Sagres if you do the Algarve.

Maybe it was just special to me because I grew up in Brazil and studied it as a kid in grade school, but everything Henrique o Navegador was special to me

Don't give up on an overnight in Sinatra, and you need at least a full day there. Lisbon is worth four full days, just a nice place to slow down and be there even though the sights are not off the charts must see. My wife and I loved Obidos but it's fine as a day trip with a car. We found it very sleepy when we visited in late September, would have been even more so after the day trippers left. We enjoyed Nazare quite a lot too. There is not much to do there but a nice place to stay after day tripping. We stayed a night in Tomar and visited the Convento de Cristo, a Templar monastery/castle. It was a little ragged in its state of repair but a nice visit in a pleasant town. The mountain top town of Marvao is situated in a spectacular setting, it's out of the way but was worth taking the long way to Evora (we went north to south). There are a lot of smaller places to discover in Portugal, and you are sure to find your own. Pinhao looks awesome too judging from Google images, though I have never been there. Porto is pretty gritty but also has charm for city of its size. The most fun for me was walking on the top tier of the bridge over the river. The views were really something. I did it after dark but wish I had the chance to also do it during the day. I think May will be a great time to visit. Portugal is a great and very underrated country to visit.