Sidewalks - public or private property?

This will vary by jurisdiction, and possibly by development, however.

Recently in Raleigh some citizens complained to the city about the terrible condition of the sidewalk in front of their home. Tree roots had forced sections of the concrete up and made the surface very uneven for walking. Their first couple of complaints went unnoticed. After being ignored, they turned up the heat and went to a local consumer reporter about it. The result was that the homeowners found, to their chagrin, that it was their responsibility to maintain. The city had been ignoring it, but, once it was brought so publicly to their attention, they cited the homeowners and told them they had to foot the bill for repairing it or be found in violation.

In Honolulu, your sidewalk belongs to you but the public has the right of way. They give limited immunity with regards to lawsuits as the city assumes this liability and repairs. The same is true if you border a river, stream, or gulch. Bad news: the city can assess to you maintenance costs!!