I don't know much about the San Antonio hotel itself other than it's located at the far end of the main strip in PDC, just before the Los Pocillos beach. The hotel has direct beach access.
I think the market you refer to is at TEGUISE and not Costa Teguise. It's a Sunday morning market and probably worth a visit once although it can get rather busy, ask at reception for details of how to get there, or even hire a car but it gets pricy for a 6 seater.
Timanfaya definitely worth visiting, note there's a place where they do a short camel ride, a Visitors Center and then the volcano itself (and coach trip), these are not all in the same place -close but it's not just one site.
PDC itself has a long strip of shops bars and restaurants, mostly on one side of the road with the beach on the other. No building is more than 2 storeys so it doesn't appear built up and billboards are not allowed.
At the far end (and around the corner a bit) is the Old Town (3.5km from S/Antonio) which is centered around a small working fishing harbourside which has several decent restaurants and a small (but well formed) shopping center which has some well known high street brands such as Mango, Zara, Footlocker, Benneton etc (I'm told it's quite cheap, especially Zara). Leave the girls in there and pop over the road to the Bus Stop bar for light refreshments.
For nightlife head towards Centro Atlantico on the strip, or for a more laid back evening any of the numerous bars and restaurants, or of course your hotel (but a shame to spend all your time there).
I daresay the teenagers will like C/Atlantico, but they can visit the younger bars/discos whilst you're enjoying some live music in Charlie's bar just a few yards away.
PDC has something to suit everyone, pick the bits you like and ignore the bits you don't and you'll have a great time.
Cheers - Ole
