I am biased as I live here but Albufeira would fit the bill. There are two distinct parts though, the old town which has just about held on to its character and the new town a mile or two away (Areais S. Joao) with its infamous 'Strip' which is wall to wall bars and restaurants catering for the hordes. Dozens of villas, hotels and apartment hotels to choose from, but be careful as some are described as 'Albufeira' when in fact they are four or five miles from town and a long way from the sea!

The whole area is very hilly, so you might not like it if you don't fancy a 15 minute steep uphill walk back to your apartment after a good night out; the lack of taxis at peak holiday times is a present bone of contention!

Beaches are mostly big and sandy, safe swimming and bathing plus plenty to do day and night with sufficient diversions not too far away eg theme parks when the girls get tired of the beach.

Countless bars and restaurants to choose from of every possible type.

(Social beach observation - the Portuguese boys and men play endless games of football 'keepy-uppy' and foot-volley all trying too look athletic etc while the girls ignore them completely and talk endlessly in groups while texting someone else.)

Hello there gally56

There are lots of nice places to stay in the Algarve with lovely beaches and excellent places for your teen girls.

I would recommend Praia da Rocha, the beachfront of Portimão. It has a lovely strip with lots of restaurants, ice cream shops, bowling, beach activities at good-looking beach, lovely Marina, etc

http://family.webshots.com/album/69875624jNefMd

Portimão is the 2nd city in the Algarve (after Faro) and has a nice shopping zone as well as a nice shopping centre with cinemas and a very pretty riverside for river boat trips up-river or to the sea.

Nearby is Ferragudo, a quaint fishing village (also with nice beaches and restaurants) and slightly further a field (within a short bus ride) is the popular village of Alvor with more restaurants and lots of nice bars.

If you decide to stay at Praia da Rocha check out Jardins da Rocha. This building is in a quiet location (yet within a stone's throw of the beach) and has a private swimming pool and tennis court.

From Praia da Rocha, you can get down to Lagos (historic town) and Monchique (great viewpoints in the mountains of the Algarve) for days out and girls will love Zoomarine (http://www.zoomarine.com) and Slide & Splash !
(http://www.slidesplash.com/index.php?lang=en

Of course there are other areas with lovely resorts which perhaps you can check out before you make up your mind:

Aljezur, Vila do Bispo, Lagos, Lagoa (including Carvoeiro & Amação de Pêra), Albufeira, Loule (inlcudingo Quinta do Lago and Vale do Lobo), Faro, Olhão, Tavira, Vila Real Santo Antonio + others!

Whatever you do have a great time in the Algarve!