You can visit Mirjan Fort in Kumta, Vibhuti Falls at Kumta and definitely you need to visit Yaana at kumta. All are within 45kms from Gokarna. if you wish to travel then you can vist Murdeshwara also.
Hey! Do visit Murudeshwar town near Gokarna. It has one of the biggest Shiva Statues in the world and a giant Gopuram with a lift inside it. On your way to Murudeshwar, you can stop at Mirjan Fort and Eco Beach and have Lunch at RNS Cafe, Murudeshwar for a great lunch with awesome sea view.