Brac is famous for its Zlatni Rat beach, pictures of which you can see everywhere in Croatian tourist literature.
If you want something less crowded and more peaceful, the village of Sutivan fits the bill. It’s only a few minutes bus ride from Supeter, the ferry terminal.
A glorious distance view of Split - especially at night - can be seen from Sutivan. It has good quality accommodation and quite a few beaches, cafes and restaurants.
I would recommend the Pizzeria Bracera; at the top of the Riva by the jetty - you can’t miss it. Good quality pizza at decent prices. The ‘Nasa More’ pizza I would recommend.
You can take excursions from Sutivan to elsewhere. The boat ‘Mali Jure’, which you can’t miss by the Riva, does fish picnics to Hvar, Trogir and Omis.