Hi
I have been to Lagos as a day trip. It's a nice town, lots of shops, cafe's etc. Didn't go to the beach. Very suitable for families.
We stayed in Praia de Luz about 15 mins drive in the car from Lagos. Liked it so much we have been twice with our two DS and we don't usually holiday in the same place twice. Didn't stay in a hotel though, we stayed in a serviced 3 bedroom penthouse apartment (second time) on a complex about 10 mins walk from the beach, cafes etc, Has adults pool, kids pool both heated and an indoor pool, gym, fab spa (had two excellent body massages). Restaurant on site. PM me if you want the details.
The first time we stayed in a house (pool not heated - you need a heated one even in Aug) with another family. Don't need a car in Luz can walk everywhere, loads of great places to eat out and a couple of supermarkets to stock up. That is if you aren't fussed about venturing further.
It has the most fantastic sandy beach (though the water is not warm) with rock pools to keep the kids happy for hours. This is good as you can send Dad to play/supervise and you can lie on the beach and relax! There is a local bus that takes you to Lagos but we didn't use it.
Transfer from airport to Luz was about 50 mins (from memory). We hired a car from the airport the first time (dire car seats so take your own) which was expensive and the second time we arranged a taxi to collect us (we took Bubblebum booster seats). We did hire a car for a few days in Luz so we could venture further (also have details for this).
PM me if you want any more details. It's a fantastic part of Portugal and incredibly family friendly.