Firstly, I should point out that the Algarve is a region about 160 kms East to West and 45 kms North to South. It is therefore not a big region and with the A22 Motorway that runs from the Spanish Border to Lagos, nowhere in the region is less than 90 minutes drive away. (traffic permitting.)
You therefore have a chance to explore the whole region. Note, however, that you will be here at the height of summer - it will be very hot and it will be packed.
I should warn you that Luz will be stuffed full - mainly with my compatriots!
Luz really has become an English/Irish Colony. There are several restaurants there. The webite is not an official website and many restaurants don't see the need for web-marketing.
The beach will also be stuffed full.
For alternative beaches I recommend exploring the following:
From Luz take the exit for Espiche, turn left onto the EN125 and continue about 20kms until you get to the cross roads for Parque da Floresta and Salema. Turn left and left again and take the road down to Salema. It is a pretty little village with a nice beach - but again will be probably busy at that time of year.
Alternatively, carry on another 8kms. to the village of Raposeira. Turn left at the lights and follow the signs for Praia da Ingrina or Zavial. It is a loop road and you can chooses which beach you prefer. In my opinion, Zavial will be the better. Again it will be pretty busy.
However, if you continue past Raposeira and turn ledt at Vila de Bispo towards Aljezur you will come after about 20kms to Carrapateira where again there is a great beach.
This part of the Algarve is full of hidden beaches but I don't have time here to list all of them.
Be aware that Portugal is a gourmet's delight. Great food here - provided you go to the local restaurants!
In Lagos try the Dom Sebastião on Rua 25 Abril and Antonio's at Praia Porto de Mos overlooking the beach. Also, for cheap and cheerful, try Até Qu'enfim behind the Intermarche Supermarket
If you are going to explore or get to hot one day, take a trip up Monchique, the small mountain that dominates the landscape behind Lagos. Great views and Scenery. Stop at the local Spa at Caldas de Monchique for coffee, 5 kms below the village of Monchique.
Carvoeiro is pretty but then so is Salema. Silves will be hot and while maybe worth a visit there is only really the Moorish Castle to see. (Only the structure and walls not a furnished castle.)
I would suggest that Lagos itself would be off more interest as it retains much of its Portuguese Character including city walls, and old buildings. Visit the museum, the old Portuguese Fort, the churches etc.
Have a look at this Wikipedia article for more:
http://en.wikipedia.org/wiki/Lagos_%28Portugal%29
As regards the "Feira de N. Sra. Da Glória", don't expect anything special - These are not Mexican or Spanish Feast Days. There may be a street parade, a couple of bands and some good food but generally in Portugal these Feiras do pale in comparisom with those of the other Ibero-Cousins.
For the kids look at Dolphn Safaris from Lagos Marina.
Also have a look at Zoomarine about 30kms from Lagos.
See:
http://www.zoomarine.com/
Note that if you are feeling flush you can arrange for about US$250 per person to swim with the Dolphins.
There are also some great waterparks here:
Try:
http://www.slidesplash.com/
for starters.
If things really get boring, take a trip one day to the Eastern Algarve (About 60 to 90 minutes drive.)
Visit:
Estoi - Roman Ruins
Tavira - delightful coastal roman town - retaining its portuguese character.
Castro Marim - Castle
and then nip over the frontier (no border controls) and have Tapas in the town centre of Ayamonte, Spain.
For further info have a look at my blog where you may find interesting nuggets:
http://barlaventostravelblog.blogspot.com/
Just out of interest who are you hiring your car from????
Lagos Shops -
Big Supermarkets - 08:30 / 09:00 thru 20:30 / 22:00
6 days per week. Sunday half day.
Small shops
09:00 to 13:00
15:00 to 19:00
Saturday half day. Closed Sundays.
I think that pretty much addresses most of your questions.
Have a great trip.
