1) Visit the little farmers market at Mancha Blancha on a Sunday. This is very much a local's market, selling only food, but there is a lovely variety: big sacks of dried anchovies, local wine in unlabelled bottles that has to be worth a try at just 3 euros each and fresh herbs and fig jam. Perfect if you are self catering, want to put together a beach picnic, or even for souvenirs.
2) Rather than take your children to one of the expensive, zoo-like theme parks on the island, I recommend you visit Pardelas Nature Park (www.pardelas-park.com) which offers an altogether more local experience. Kids can actually interact with the animals, rather than just looking at them in cages, learn about the local flora and fauna, and even try their hand at pottery.
3) I would always suggest trying to arrange your trip to see the Fiesta Nuestra SeƱora de Los Dolores in September – Lanzarote's most colourful festival is a wonderful mix of folklore, history and fun. It is a delightful insight into local life, during which islanders, many of them dressed in traditional costumes, make a pilgrimage from all over Lanzarote to give thanks to the Virgen de los Dolores, the patron saint of Lanzarote and the 'Lady of the Volcanoes'. Travelling on foot with donkeys and camels pulling carts laden with food and drink, the processions are a wonderful sight, ending at the church in the tiny village of Mancha Blanca.
If you are after the latest, up to date information about the island, make sure to look at www.lanzaroteguidebook.com It really is comprehensive and in-depth and one of the best online guides I have read.