You can buy tickets online or at the Old Town entrances to walk the Old Town City Walls. This is the best way to explore the Old Town and enjoy spectacular views. Recommend doing this early morning or at sunset to avoid the heat.
Mljet Island is an easy day trip from Dubrovnik by ferry or another chartered boat. It features the beautiful Mljet National Park, which is an absolute must-see! Beautiful preserved nature park where you can bike, walk, swim and explore 2 lakes and an island (within an island). Eddy and I visited the park together in July '21!
The Elaphiti Islands is a small archipelago consisting of several islands stretching northwest of Dubrovnik, in the Adriatic Sea. Only three of them, Kolocep, Lopud and Sipan, are inhabited and have tourism amenities. Lopud features one of the only true sandy beaches in the area. There are many travel companies offering organized boat trips to explore the Elaphiti Islands or you can arrange a private boat tour.
Peljesac peninsula is about a 1 hr drive from Dubrovnik - famous for its vineyards and its historical town of Ston.. It features the best oysters in Croatia (you can tour local oyster farms by boat) and has some of the best wineries in the region. Make sure to have lunch or dinner at either Kapetanova Kuca or Bota Sare in Mali Ston. Spend the day exploring the wineries, like Matusko, Korta Katarina.