I would suggest you visit both these places as early in the day as possible. The earlier you reach, the better as you can avoid crowds. I was told that entry is open from 6am and closes by 6pm. There is also a musuem that you will find on the way to the Bhootnath Temple, the museum is also worth a visit if you are interested in knowing about the history of the area. Entry fee to all temples and museums range from Rs. 5 to Rs. 50 per person for Indians.
Soon after, I planned on leaving to Hampi but wasn't sure on how to get there. Spoke to the manager at Krishna Villa, he said that I could either change 3 buses i.e. Badami - Gadag - Hospet - Hampi or I could take a direct taxi which would cost Rs. 4,500 as I would be charged both ways even if I only wanted to get dropped one way. I wasn't willing to do the bus as my legs were already sore from all the steps climbing I did at the fort in Aihole and Badami caves the following morning neither was I wanting to spend 4.5K. So I spoke to my auto driver to see if he was willing to drop me to Hampi and he agreed to do this at Rs. 3,200! Hampi is about 150KMS from away Badami. I quickly had Poha that was complimentary at Krishna Villa, checked out and in no time was en route Hampi in an Auto!
I started at 10am, the ride quite smooth except for a few parts where the roads weren't good. I was expecting to be there by 1pm but then I reached 3pm! Nagaraj my auto driver was really a gem, he was disappointed that he delayed my arrival at Hampi but I assured him that wasn't too late!