The southern half of La Aldea beach is pebbly and most people look at it from the adjacent restaurant terraces rather than sitting on it. The northern half is where the locals go to sunbathe because it's sandier and sheltered by the harbour wall. Just walk through the tunnel and hope there's a free patch of sand amongst the pebbles.
If you make it to La Aldea, it's definitely worth heading down to the shore before tackling the next section of windy road (all roads around here are windy). Walk south along the shore to see the famous La Aldea lagoon, site of one Gran Canaria's top crazy fiestas, then come back to the restaurants for a drink or basic lunch.
There are no facilities but if you buy a coffee, the bars let you use their bathrooms (provided that you're not wet or covered in sand).
Get to La Aldea via the GC 200 west coast road. Once in town, follow the signs for the beach and harbour.