Bit of a trek from Villamoura, but Zavial is one of the best.  Got a great bar as well as surfing possibilities!

Also Mia Praia at Lagos as the nightlife and restaurants are terrific once the sun goes down.

Enjoy.

There aren't any near Villamoura (that I could find), but if you have a car, try Zavial (about 45-50 minutes west down the motorway) or Praia Grande (west of Albufiera) but look out out for the pervs and stay in the dunes because the police wander down the beach!
Otherwise, it is Tavira (east of Faro), an official beach, which you get to by boat.

nice one. im hiring a car while im over there, so will definately go and try to find Zavial. I did a search online and it does look good!

Zavial is great!
Parking on the approach road is easy, then walk down the boardwalk to the bar/restaurant, down the steps onto the beach and head east.
The naturist area is between the small promotory and the main headland.
If the tide is out, you can walk (further east) around the headland onto a beautiful beach which has wonderful rock formations; watch the tide though, if it comes in you will have to climb back over the rocks (painful on the feet!)

sorry everyone but didnt ,manage to get to any of the nudist beaches. I managed to get my wife to want to try it, but once we found where they were, they were over an hrs drive away, and with her being pregnant, she didnt want to go that far :'(. Upside, i managed to get a few hrs nudist bathing on the sun trrace with her trying it as well, but it was too hot up there with no wind, and no chance of just jumping in th swimming pool with out having to get dressed and walking down to it. so another holiday coming back with a white arse again!lol. Maybe next time!

Praia do Gavial is IMHO the nicest of the beaches, and well worth the drive. Its about 45 mins west of Vilamoura and is a great location, including a fabulous restaurant just overlooking the beach.