Hey Worthington (is your name after the bitter or something else) .... Whenever I've been out with friends in Costa Teguise we always head down to the square off the start off the Avenida De Las Islas Canarias
http://maps.google.co.uk/maps?hl=en-GB&ie=UTF8&q=costa+teguise&ll=28.996439,-13.491136&spn=0.004298,0.009978&z=17&om=0 and go to Chispas (which is a tiny litle bar with only 10 seats inside ... but great prices) ... you'll find a lot of the young locals meet there before going further on their night out!
There are lots of good bars in Costa Teguise which cater for all so let us know what you want from your nightlife ... pool table, karaoke, dancefloor, chillout, cocktails, pints of Worthingtons?

? ... let us know more and then sure someone will tell you their favourite!
Phil