Iolani Palace is my favorite place to take visitors and easily accessible by bus. While there, it’s right across the street from the free State Art Museum, and St. Andrew’s Cathedral with spectacular stained glass windows is only a block away.
My favorite beach is Kaimana Beach at the Diamond Head end of Waikiki just past the Waikiki Aquarium which is also fun.
The Honolulu Museum of Art has many lovely exhibits and is reasonably priced.
There is one important note. The USS Arizona Memorial is closed due to needed repairs at the dock to enter. It is scheduled to reopen some time in March. There is still an extremely good movie to view at the site where you get on the boat to take a little tour around the area where the ship rests on the floor of the harbor. It shouldn’t be missed.
Our bus system is very good. When you get on the first bus of the day, you pay $5.50 and ask for a 1-day pass, which you then use all day for as many rides as you want. The bus drivers are very helpful and will tell you what you need to know to get to your destination.
@Kardamom has given some good information. There’s one change. The International Marketplace has been completely rebuilt and is now a high-end mall of sorts. You can sometimes watch hula there, but it is not the simple market is was once. It is anchored by Saks Fifth Avenue.