Campo Internacional, the main part of the resort, is a big place so be prepared for some walking. Depending on where you are in Maspalomas you're looking at up to half an hour's walk down to the beach (if you're in Sonnenland, or further away from the sea than Holiday World, get a taxi). If you walk, head to the dry channel that runs through the middle of the resort and follow it.
You'll go past the camels, where you can book a ride through the dunes, and arrive at the famous Charco de Maspalomas lagoon and then the beach itself. Turn left to walk along the sand towards the dunes and Playa del Inglés. It's about 6 kilometres one way but there are snack stands on the beach. If you want a fantastic meal, then book a table at Samsara on the top of the little shopping centre by the lagoon. It's fantastic!
For a more relaxed first experience turn right at the lagoon to see the Faro de Maspalomas lighthouse and the long boulevard that runs along the coast to Meloneras beach. Choose a terrace for a drink and a meal or stock up in the supermarkets. Just behind the beachfront there's plenty more shops and restaurants.
Away from the beach Maspalomas is mostly hotels and bungalows but there are some things to visit. The huge park next to Holiday World is a fantastic spot for a stroll or a jog and even has its own lake. Maspalomas even has its own Botanical Garden full or tropical fruit and flowers. Head to Avda. del Touroperador Neckermann. The garden is right by the big roundabout. Entrance is free. Holiday world itself offers bowling, fairground rides and a vast range of arcade games for the kids.