I think the Old Town of Albufeira would be ideal for you. It's lively and fun but very family orientated. There are lots of bars and good restaurants there, and two nice beaches. It's easy to get excursions to other places in the Algarve, or if you hire a car you can explore the many places of interest including the countless beaches and coves for which the Algarve is famous. There are waterparks, zebra safaris, boat trips and water sports.

Wherever you choose, I hope this trip will be the first of many!

Take a look HERE josisbowe.
It's right on the beach and is within walking distance of what you are maybe after.

Robby

The other place you might like to consider is Lagos, i'm thinking of going with a 12 and 14 year old. It's probably not quite as lively as Albufeira. But in the school hols should be busy enough. Loads of good restaurants, nice beach. The apartments i've been considering are:-

Marina Park (they have both 1 & 2 beds)(airtours)
Vilabranca (ditto) (thomson)
Marina Club (could only find 1 beds)

The first 2 you can book through tour operators, Marina Club(which seem quite upmarket) seem only to come up on DIY with people like http://www.wintersunshineholidays.com

They all seem to have good reports. But you would need to research to see if the locations were good for you.
Good Luck.