In Lanzarote? You can travel the whole island it's so teeny, in lanzarote generally you have to go to jameos del agua it's this really cool place with albino crabs that are the only ones in the WORLD. Think the water park is good too, and timanfaya is worth a day out. As for costa teguise, can't remember what it's called but there is the most excellent pizza place that has a parrot and they serve beer in massive glass boots. Very cool. When you going? only i'm going out in november!
Can`t do better than becks advice.
Hire a car and take in the whole island.
The beaches in the North are fantastic for surfing and La Mirador viewpoint is spectacular.
Unfortunately because the island is so small I found that 1 week was long enough for me but I`m well past the nightclubbing age. Then again, I`ve been twice so I`m contradicting myself.
Watch out for rip-off prices for coach trips if you don`t drive......a group can hire a taxi for the full day a lot cheaper.