Kuta is a good base for exploring south Bali. The cliffs and sea temple at Uluwatu are an easy half-day, the seafood grills at Jimbaran an evening, and the cultural heart of the island at Ubud is an hour inland and worth a full day even on a quick stop.
Further afield, the volcanoes of Mount Batur and Mount Agung can be done as long day trips with an early start — a driver from Kuta will pick you up at four in the morning for the sunrise hike up Batur and have you back by lunch.