If you instead prefer to take a nice walk in the forest you should go to “Kungsbackaskogen”. It’s in the north of the city, just 15 minutes walk from the train-station. There is a path inside the forest, 2,5-3 kilometers long, where you can run for a while, or just relax and walk around in the nature.
Beautiful scenery, no matter at what time of the year you'll come. In the middle you'll also find a huge pond.
Kungsbacka is close to the coast, and inside the city center the Kungsbacka river flows. If you’re looking to take a bath in Kattegatt, the ocean on the west side of Sweden, you’ll just have to go 7-8 kilometers south from Kungsbacka. One hour by foot, 10 minutes by car. You shouldn't expect a beach, but it's nice to swim and jump from the cliffs.
If you instead are looking for the beach you’ll have to go to Åsa, 15 kilometers south of Kungsbacka. There are buses going there from the trainstation in Kungsbacka, bus number 732 goes directly.