If your legs aren't too worn out from exploring the old city walls, head south past Ploce for a peek at Croatia's natural beauty and recent war history. Walk for about a mile along a flat road lined with fancy boutique resorts and villas.
Sveti Jakov Beach (which my inner 12 year-old would like to mention sounds like "sweaty jagoff" when said out loud).
Lokrum Island in the distance.
photos of the hotel and its graffiti if you're curious.