Portugal - 12 days Help!

We are planning a trip of 21 days in September 2017. I have spent a lot of time thinking and planning.

I would spend my time in Lisboa, Coimbra, Porto.
I would not go to the Algarve. It is full of English tourists, far from Lisboa. It has beaches and pubs and not much else.
Spend at least a few nights in each hotel so you don't feel as if all you do is pack/unpack.
If you really want a beach, then consider Figueira da Foz which is just 1 hour via train west of Coimbra. Another beach alternative is Aveiro which is halfway between Coimbra and Porto.

Minimize travel time. It is wasted time.
Maximize time in each location so you can relax and get to know the city.
Bigger cities have good/great food. Lisboa, Porto, Coimbra. Smaller places (beach towns) have fewer excellent restaurants.
Spend some money on tours. Everyone says it is worth it.

I found a great free planning tool at https://www.planapple.com

Yes, you are trying to cram in too much, IMO! I agree with skipping the Algarve this trip. It does have lovely beaches and rock formations but not a lot else. You can find beaches much closer to Lisbon if you want a beach fix. I agree with the previous poster that Foz is nice but Cascais has a couple of decent small beaches, it's so much closer to Lisbon and can be reached easily by commuter train.

In 12 days, I would aim for no more than three overnight places to cut down on travel time. If you haven't booked your flights, you might fly into Porto and out of Lisbon. I did that on my scouting trip before moving here and it worked great. You can take the train easily and cheaply between Lisbon and Porto and that's much more relaxing than driving. It's possible to train from either Lisbon or Porto and stop in Coimbra, rent a car and drive to Obidos. Don't try driving in Lisbon! Or, taking a small group tour from Lisbon to Obidos is also possible. IMO, Obidos is not worth more than a morning or afternoon.

Outdoor cafes are plentiful in Porto and Lisbon (and most other places), so relaxing while eating and/or drinking great, inexpensive Portuguese wine is a great way to spend time and soak up this lovely country. There are great party areas in Lisbon, also. If you are here on June 12, the feast of Sao Antonio is a great street party in the Alfama area of Lisbon.

Thanks for much for your insights. Unfortunately our flights are booked, we found an unbelievable price (roughly 400$) from Canada to Portugal so we can't switch the entry and exit locations.

In terms of Evora and Coimbra, I've heard mixed reviews of both places where many people say its overrated and not worth going if you are going to Lisbon/Porto. What are your thoughts? Alternatively, many have said that Marvao or Monsanto are also good alternatives.

The pictures of the Algarve are really gorgeous, so I was really hoping to see the beaches. Would I be wasting a lot of time flying between Porto and Faro and then driving/bussing/training around the Algarve?

Since your flights are booked and you really want to see the Algarve, you might want to think about skipping Porto. You could then do the Lisbon area, see Obidos and Sintra then spend a few days in the Algarve. Lagos is my pick to stay in the Algarve and you will want a car. The busses are infrequent so would really waste your time. Tavira and Sagres are both too far from everything and Lagos has the best rock formations IMO.
If you must do Porto, don't return to Lisbon before going from Obidos to Porto. You should be able to get transport to Coimbra ( or some other town on train line) and go to Porto. A trip up the Douro is nice if you go to Porto. We did a small van tour that went to a couple of wineries and a port quinta that was a great way to see the area.

Thanks for all your help! How about this revised itinerary:

June 17-21: Lisbon (with one day trip to Sintra and another to Cascias/Belem)
June 22: Bus to Obidos or Train to Coimbra
June 23-25: Train to Porto (Sao Joao Festival)
June 25-28: Fly to Lagos (rent car and see multiple places around the Algarve)
June 28: Fly from Porto to Lisbon to catch flight home

What day are you flying back home--the 28th or the 29th? If it's the 28th, I would want to spend the night of the 27th in Lisbon.

I went to Portugal last summer, and we did 3 weeks in the area. 10 days in Lisbon and 11 in the Algarve. The beaches in that area are spectacular, and we were content to explore the different coves and cliff beaches each day. I suggest renting a car to give you a little more freedom. We visited Cascais from Lisbon, and it was cute, but not incredible. Very crowded. Loved Sintra. As for the Algarve, we loved Sagres and Lagos. I was originally planning to do Evora from the Algarve as a daytrip, but we ended up wanting to visit more beaches instead. While the beaches do kind of look the same, many of them are known for different things. We found one that had great tide pools during low tide, one great for shelling, one for seaglass, one really enormous famous beach, many great for swimming, and so on.