Spanish River Park is the quieter alternative to Red Reef, with beach access, picnic areas, trails through coastal vegetation, and shade from sea grape and Australian pine. It feels more like a local park than a visitor attraction, which is exactly why it works.
The park is good for a low-key morning: swim, walk the dunes, then retreat before the afternoon heat. It is also useful if you are travelling with children or want more space than the central beach access points provide.