A tough choice between the north end of Howrah Beach on the Eastern Shore and Okines Beach near Dodges Ferry. Both have wonderful shores to explore and view all sorts of sea life and plants. Both are generally safe with easy access.
Tinderbox is a small beach south of Hobart, ideal for learning to snorkel. There are lots of underwater features to explore, and there are good amenities and parking. I also recommend the east end of Howrah Beach around the rocks.
Bellerive Beach. A great beach and fun park combined with excellent facilities including BBQ areas. This is an ideal location for kids and birthday parties and caters well for people with disabilities.
Hope Beach: On South Arm Road, this beach has great sand dunes and an incredible beach that is usually free of other people. It often has good surf. For a potentially wild and open beach not far from Hobart, this is it.