I would recommend climbing Diamond Head in the morning. Early morning.
It gets warm and sunny very quickly
would recommend to walk back into Waikiki from Diamond Head.
there are a few nice "local shops and places for eating" along the way
I know there is a bus that goes around the island of Oahu. May be a lot cheaper than to rent a car.
Parking everywhere is expensive and parking on the street comes with lots of restrictions.
Inside Honolulu take the bus or Uber
I like the luau at the Royal Hawaiian. It is anything but inexpensive. Hilton Village also has a rooftop luau (or used to)
Walk along Kuhio Avenue if you want to try some food stands/smaller food places. Much cheaper.