Dias beach is a bit of a hike down from the funicular, but well worth it. It is deserted. It is a truly spectacular beach - you sink 2 feet into the sand when you get off the steep steps. Look out for all the dasi (kind of like cute gophers) on the steps down - you are surrounded by them.
Last year we went into the water - and this has to be the most dangerous beach I've ever been to. The surf was crashing in with about 6 ft waves. We didn't go in past out knees - but there was 4 feet of foam and the undertow was wicked, both the foam and undertow knock you down. An awesome sight this beach is.