Since everything is located in Old Town, walking is the best option. However, there is public transportation available if needed. Bus tickets cost 15 kuna and taxis are also available.
If you have more time, consider visiting Lokrum Island or take a cable car up to Mount Srd. For a shorter trip, you can skip the sea kayaking activity. Also, wear comfortable walking shoes and bring a water bottle to stay hydrated. Lastly, be sure to bring cash as some places do not accept credit cards.