The Bjäre peninsula is littered with ancient burial mounds. The largest one is just south of Torekov along the sea but there are plenty of others which a good map with heritage signs will show you. If you haven't got a map, you will still see them everywhere in fields as you drive or cycle along the countryside.
Gröthögarna is an amazing collection of seven low burial mounds in a nature reserve next to the sea. You find them just north of Torekov golf course. The nature reserve itself is quite nice with seaside views and sometimes grazing cows.
Most people that visit Bastad never drive further out on the Peninsula. I would strongly suggest to do so. It will show some amazing Swedish landscape.
Follow the signs to Hovs Hallar. It feels like you're at the tip of the peninsula, which you aren't. This place consists of a moorish type landscape with paths leading you to the ocean. Here the coast is all about cliffs and rocks. It's very rugged and beautiful. It's also a popular spot for hiking.