Halebidu and Belur are small towns near Hassan city. Tourists usually stay in Hassan city and reach one of these places first and go to the other before getting back to Hassan. There are buses every ten or fifteen minutes to Halebid from/to Hassan which is 28km and 45mins away while there is a bus every half an hour from/to Belur.
You can get a government bus for 25 rupees from Banavara, itself on a major highway and easily accessible from many major intercity bus lines.
Food at Halebidu might be a problem if you are not a south Indian. Hence it is better to carry food from Hassan or reach Belur.
You can stay in a larger town nearby such as Hassan or you can stay in the town itself.