Best day trip on archipelago?

We are a couple and a toddler (3). We have a car so don’t need to travel from Stockholm directly.

We have a full day tomorrow to travel somewhere in the archipelago.

So far our research means we are avoiding Vaxholm as it’ll be too crowded and not a ‘true archipelago’ experience.

Utö or Sandhamn are leading the race. Any advice?

Culture, nature and maybe a swimming spot are our criteria.