If you want to go for a swim you could choose between the sea, a lake or a public swimbath.

Kungsbacka:
https://www.kungsbacka.se/Uppleva-och-gora/Simma-och-bada/Badplatser/
(unfortunately in Swedish but the ones with the bold text is the names, so google them).
Our favorite spot is Vickan, which is a small place by the sea that not so many people are aware of, so less croweded than other places.

Stora Iglakärr is a nice lake (according to Mias dad who took the kids there recently).
https://www.badkartan.se/Kungsbacka/

Gothenburg:
The sea:
Take the ferry out the archipelago (see that post for more details)
Lillebybadet, Torslanda
Sillvik, Torslanda
Askimsbadet, Askim
Hovåsbadet

A lake:
The closest one within walk or biking distance is Härlanda tjärn or Stora Delsjön.
Nicer place Aspen, Lerum (20 min by car)

Public bath:
Kungsbacka has a really nice and almost new (opened 1 or 2 years ago) indoor swimbaths with  water slides , a 50 m swim pool with trampolines and relax area.
https://www.medley.se/kungsbacka-badhus/bad/
(only in Swedish, but use Google translate or similar)

Åbybadet, Mölndal
https://www.molndal.se/abybadet.html
(brand new, we haven’t been there)

Vattenpalatset, Lerum

Look them up here (swedish page, but you can get where they are), or in Google maps:
http://www.badkartan.se/G%C3%B6teborg/