Eight nights in October—enough time for Lisbon, the Algarve, and Porto?

Definitely go with option 2!

You can barely do justice to two places in 8 nights. Even though Belem is a part of Lisbon, it takes most of a day to see everything there. And, you can easily fill the rest of the time in Lisbon itself, especially with one day out to see Sintra.

I too would recommend option 2, perhaps with one of the five Lisbon nights transferred to Porto. "Three nights" means only two full (non-travel) days, and "two nights" means only one full day -- I'm not sure what the point would even be. Note, too, that while Lisbon and Porto are cities, the Algarve is a region, about the size of Delaware.
Also if, as in option 2, you spend four full days in Lisbon, with one day devoted to Sintra, you may not need additional day trips -- you can easily fill those remaining three days in Lisbon itself.

Definitely option 2. I wouldn’t even attempt option 1 with a 2 week timeframe.

By October, some of the restaurants in the Algarve will have closed for the winter, as the weather is likely to have turned. I have been to the Algarve numerous times, as it’s my default summer beach destination, but other than golf, it’s a one trick pony. There is so much more to see between Lisbon and Porto, so stick to this area. You could actually just stay in Lisbon and take day trips to Cascais, Sintra and Evora, but Porto is good too, including the Douro.

In the Algarve, Tavira and Lagos are the best places to stay. I would avoid Albufeira at all costs, as it’s been ruined by drunks on stag and hen parties. Salema has been ruined by over development and now there is nothing to distinguish it from Luz, Burgau or any other resort along the coast. Several restaurants will be closed and it has a sleepy feel in October. You really need a car to explore the Algarve.

The answer depends on your travel style. I would recommend the second option. We visited the "silver coast" beach area of Praia de Viera in June and I did not care for it, but the Guicino beach between Cascais and Sintra was beautiful. The drive Lisbon to Lagos in the Algarve is 3 hours each direction. So you basically take up 2 days with getting/dropping off rental car as you need a car in the Algarve, driving, checking in/out of your lodgings. With 8 nights you could easily find plenty to do in Lisbon area (Lisbon has so many different areas to enjoy just within the city itself: gardens, museums, sports stadiums, cultural/historic sites, new urban and revitalized areas, a river, music, art, food, wine from both Lisbon area vineyards and from all over Portugal). I would highly recommend you consider spending 8 nights in Lisbon or 6 nights in Lisbon and 2 in Sintra (There are just no words to describe how magical the little bit of Sintra that I saw was).

Happy Travels!

Thanks everyone! Appreciate the feedback and tips—we are going ahead with skipping the Algarve on this trip and staying focused on Lisbon, Sintra, and Porto.

Cheers!