For Oahu, Honolulu, I would go to Pearl Harbor if history is your thing. You need to get there early to get to the memorial, there is always people going, probably around 7 to be done by 10.
Luaus are fun, hit one up there like another poster said, if you don't like alcohol, want to go to a dry luau, Polynesian Cultural Center has one. Heard it is really good experience, lots of history. Believe this is an all day thing, not sure though.
We went to Paradise Cove. It was pretty cool. They start around 4 and have a few things to do, like Hula lessons, making bracelets and things and a cove canoe ride and fish net hauling demo. At dusk they start the show and have dinner. First they present the Prince and Princess or King and Queen, forget which, the pig, which is cooked in a pit. Then have the fire dancing and stuff as a stage show while eating. I recommend going with the cheap package for seats, as you sit with everyone and get the experience. If you want a more intimate time, the expensive package seats you at a table for 8-10, so probably you and another party. You also get your food brought to you and a couple drink coupons.
If you like museums, I really enjoyed the Iaolani Palace. Takes about an hour and is self guided. This tour really points out the last days of the Hawaiian Kingdom and is interesting in that respect. You might also watch Princess Iolani before leaving home, just to have a little more background.
Bishop Museum was also pretty awesome, especially the Hawaiian building. The rest of Bishop is like stuff you see anywhere else. Probably expect to spend half a day at Bishop if you want to just go through the Hawaiian history building, all day could easily be spent there. When we went, they had an interesting Hawaiian Shirt Exhibit. Also have a pretty cool Geology exhibit where you go through a volcano. Meant for kids, so you can hit it up in maybe 10-15 minutes, plus the time of the movie.
Plantation Village is fun, they have some good history there, explains the culture of the islands and has some local fruit tasting at the end. Probably takes about a half a day and is outside Honolulu. Really thought it was a little long, but has a nice blend of the history if the cultures that came to the islands and explains why one of the Hawaiian restaurant chains has Bangers and Eggs/something on the menu.
The Mission Houses was an alright tour, seeing New England style houses in downtown Honolulu is kinda cool. These are also pretty close to Iolani Palace and the tour is about an hour. You learn about some of the mistakes the early white people to the islands made in architecture and stuff, so that is kinda cool.
For shopping, if you are on the island on Wednesday, Saturday or Sunday, Aloha Stadium has a flea market. There are tons of stalls with a ton of souvenir type stuff all pretty cheap. Starts pretty early and the stadium is kinda far from Honolulu, in Aeia, maybe 15-20 minute drive from Waikiki.
There are tons of shops around to get stuff as well. ABC stores have a ton of stuff and International Market does as well, though a little more expensive then the flea market. International Market also has Hanks Hawt Dogs, lots of cool types of dogs, just get there around lunch if you want Alligator dogs. My favorite noodle bar is down around there as well, get some Udon and half boiled tempura eggs really cheap.
Speaking of food, my favorite breakfast, for the price, was Koa Pancake House. They are about the same price as IHOP on the mainland (who is higher than near Disneyland prices on the island, like $15 plates) with a fantastic menu. Recommend listening to Jack Johnson's 'Banana Pancakes' then getting a plate of those.
Yummy's is good Korean food on the island. In Honolulu you will find tons of touristy spots to eat as well, just choose one. Heads up, Saimin (ramen) at McDonalds is trash, but the seasonal pies are fantastic. Stop by and grab one, especially if it is Taro pie.
Also, make sure you get a shaved ice with ice cream. It is great for an afternoon refresher. My daughter really enjoyed the Rainbow ones. And stop in 7-11 and get Spam Musubi.
The zoo is just a zoo. I don't remember seeing anything there that was really native or seeing anything that was memorable. Sea Life Park was also a let down to me. But, if you want to swim with dolphins, guaranteed, they have it.
Once again, I would do all the touristy stuff here. Wakiki is pretty, but the surf is pretty lame and really busy. Might be a nice place to get a beginner surf lesson if it is cheap, but is so crowded you probably don't want to surf there if you have surfed before. Snorkeling is also kind of the same on the island, if your going to a different island do these there.
North Shore is also pretty nice, and if you have dates, I would see if you can check a surf competition. If it is winter, I would also make sure to go up there just to see Pipeline wave and check out the surfers. Especially if you have tried surfing and have caught a wave, makes you appreciate it that much more.
Also, you should try to plan at least one day to ride The Bus if you aren't renting a car, just to check out the whole island. There is a guide you can get that has plans all made out for you on Bus tours. It is public transit, so don't be looking like too much of a tourist, but it can be fun. If you have a car, make sure to take the H-3, really a beautiful drive.
Looks like this is pretty long right now, but hope it gives you some ideas. I really hope you hit at least one museum, just to get a little more understanding if the culture if the islands. As long as you are in Honolulu and it is before ten, I wouldn't be too afraid to go to anyplace, but after ten I would stay near the hotels or be doing touristy things (luau or whatever) just to make sure you don't wander into anyplace too seedy. Never had problems there, but there are big city crimes just like anywhere else.