Yes do the walls, takes around 1hr to get round, some nice views too. We got on before they closed the gates for the night so just around sunset, so it was very nice.
Plenty of sea swimming areas, all cordoned off and have ladders into the sea. We got some of those booties from Decathlon as there’s not many beach areas and you swim off the rocks in a lot of places. Miljet is beautiful and once you get there you can walk up the hill and there’s a lovely lake for more swimming / paddling.
Back in Dubrovnik there’s plenty to do , things to see and go, just have a wonder through the streets. I can recommend a restaurant called Pizza Mia Culpa. It serves Pizza / Italian but so cheap and a pizza as big as the moon ( I exaggerate…slightly) for about 8 euros!
Public Transport is very good there too and handy for getting about. If you have time i’d also suggest a boat ride to Hvar. Thats lovely too. I like Croatia and Dubrovnik a lot, been there twice. Have fun.