Luz town is small but has a lovely selection of restaurants (some of our favourites are The Dolphin and Fortaleza). Luz beach is a Blue Flag beach, so the sand is clean and the water is safe. It also has a really nice promenade.
There isn't much in the way of night life in town but you can get the bus into Lagos but will probably need to get a taxi back as the buses don't run till late at night. There are lots of other beaches to explore in Lagos - Praia Dona Ana and nearby beaches have sheltered coves which are great for a windy day. If you don't like waiting for the bus or want to explore further afield then you would need to hire a car.