HELP Family Travel Advice. Algarve??

Lagos has a small airfield but not an international airport , the nearest one is in the city of Faro about 1 hour away.

Salema is really small - originally was even smaller but a bunch of tourist vacation homes have been built due to the notoriety of travel writers.
Lagos is a better choice, the bigger beach is on the other side of the river but you have a car to get there.

There are some beaches near Lisbon if you don't want to drive to the Algarve.
https://www.cascais-portugal.com/Guides/cascais-beaches-beach.html

Edit: because you mention Lagos airport fyi Lagos is also the name of the largest city in Nigeria, Africa, when doing flight searches it might come up.

Definitely stay in Lagos instead of Salema. There very little there other than the beach and high rise apartments. Why RS still recommends it is beyond me.

The other poster had a great point about beaches closer to Lisbon. You might want to google Silver Coast Portugal, for beaches in that area. Cities like Ericeira are big enough to have restaurants but still retain Portuguese charm much more than the Algarve. There are a number of places of interest in the Silver coast area like Alcobaca and Batalha. Much more history in that area also.

Goodness thank you both SO MUCH! Sounds like I'll plan to stay closer to Lisbon and fly out from there. We are meeting in Lisbon, still looking for a moderately priced (400? night?) lodging in Lisbon, trying to determine which neighborhood will allow kids to walk at night to entertainment.

Should we rent a van for a few nights to see Cascais? Stay there?

Thank you, Nancy

When in Cascais we stay at Hotel Baia.
https://www.hotelbaia.com/m/en/
Word of caution if booking: there are hotels with the same name in other countries ( ex: Brasil).

You can take the train from Lisbon to Cascais, it's about 1 hour.
You don't need a vehicle inside Lisbon or to visit Cascais but having one allows you to visit other areas easier.
There's a road along the coastline starting in Lisbon going to Cascais and behond with beaches to explore.

Definitely take the train to Cascais. The parking here is challenging, especially with a large vehicle. The parking garages have small spaces and I would never want to try to park a van in one. Same goes for the few above ground parking lots in town.

The buses in Cascais are great and reasonably priced. Plus, you could take two Ubers if you wanted to go further outside of town. And, if you wanted to explore the other small towns between here and Lisbon, the train stops at all the main towns.
Staying in Cascais would eliminate the need to rent a vehicle, whereas staying someplace further up the coast you would need one.

Be aware, late October may have some rain, but the temperatures are usually still quite nice.

thank you so much. The train sounds perfect!

while I've got such expert advice, the last detail I'm trying to figure out is how to get five people from Sevilla to Lisbon without flying. It looks like the bus and the train combination will take 10 hours. Renting a car is $1500 or so. The tuk tuk company in Lisbon said they will pick us up and drive us for about €1100 with stop along the way - at this point that seems like the best option though expensive perhaps more comfortable in a larger vehicle. am I missing something?

The fastest bus between Lisbon and Sevilla is about 6 hours , the cheapest fare 22 euros per person one way.
Rede expressos is the Portuguese national bus company, sometimes they share routes with other companies such as Alsa ( Spanish company).
Driving a private car will take the same time.
Tickets can be purchased a maximum of 30 days before departure.
https://rede-expressos.pt/en/timetables

The train will take the longest and will require several transfers ( there's no direct train).

Flying is 1 hour, there are discount airlines such as Ryanair ( they're have uncomfortable seats and have extra fees for everything).

You might check out Flixbus and Gypsyy buses. They would be significantly cheaper.