I enjoyed Badija a lot. It’s got enough area that you can find a little stretch to yourself, with nice shaded spaces in the pine trees. The water is crystal clear and the view is amazing. At the dock, there are a bunch of docile black deer that come up to you for pets and treats. Recommend.
Stupe island is not worth it generally. It is basically ONLY the expensive Moro restaurant. The swimming area rents chairs and blasts music, but on the plus side has some excellent snorkeling. Rich folks in fancy catamarans hang out offshore and come in for drinks. It felt like I was cosplaying as a millionaire, which is not my jam. The taxi companies won’t come out there on a regular schedule, so when you’re ready to leave you have to call them for a pickup.
I know you asked about the islands, but if you’re stopping at the wineries outside Lumbarda town I gotta throw a recommendation for Sabulum winery. Very nice wine, tasty food, stunning views and terrific owners.