It is true that the local buses run on Palani Road, which is 3/10 of a mile from the house. However, there is no bus stop visible and Palani road has no walking curb or sidewalk. The closest official bus stop is Kealakehe that I mention two paragraphs below.
Our bus schedules are available on-line and the inter-city Kona route is here: http://www.hawaii-county.com/mass_transit/heleonbus.html#intra-Kona
I see only one pickup from the airport and that is 4:50AM. The closest bus stop to the house would be the one called "Kealakehe" which is on the South Bound Schedule. That is approximately 3/4 of a mile going north (down toward the city itself).
Kailua is naturally hilly and spread out. For the best experience renting a car would be advisable. Many of our roads do not have sidewalks.
If you find lodging downtown you can walk but are restricted to the tourist section and would miss a great deal of what there is to see. We have scores of beaches, parks, independent shops but they are spread out and it would not be practical to walk back and forth.
For those who arrive at the airport, there are car rental facilities right at the airport. For those who get to the rental, Enterprise Rent A Car will come to you with a rental if you use their service.