Theres so much to do here - if your the type that wants to see things and not only bake in the sun then my first tip is get out of Waikiki. If all you wanted was baking in the sun, Majorca would've been a lot cheaper and would leave you with less jetlag.
So quick list: North Shore - massive surf, don't even kid yourself that you're hard enough, Tantalus - up behind the university, mountain pass great views, Diamond Head - tough walk to the top, up the inside of an extinct vocano and well worth it, Makaha - quite barren part where the poor of the island have been relegated, though at the end of the road you can sometimes see whales playing offshore, Hanuama Bay - reefs, snorkelling, massive number of tourists (hence reef mostly dead).. Oh and the Toilet Bowl!!! Read here - http://www2.hawaii.edu/~turner/oahu/hanauma.htm.
Pineapple fields everywhere, military bases all over, skyscrapers and American big city hustle bustle in town, Universities, schools, gangs. The zoo (near Waikiki) is supposed to be good. Ala Moana has good shopping, a great food court and relaxing beaches - here the waves are much more forgiving and manageable. Buying anything in Waikiki is not reccommended unless you're quite happy parting with twice as much as you needed to. Buy it in the big malls or outside of Waikiki and you've save money and get better quality.
If you do want to try some bigger waves, make sure you don't go to ones with reefs. Waimea usually has good surf on a pure sand beach, there's also a cliff edge that people routinely leap from. Makapuu has Sea Life park - a sort of dolphin and killer whale zoo/circus act thing. But the waves here are also quite demanding - all sand as well, though strong currents and violent water. Be warned.
For more shopping Pearl City has plenty, for culture there's grass skirt type re-enactments up at Waimea Falls and further on past the North Shore somewhere.
Pali Highway is a great drive (goes up and over the main mountain range separating the east from the centre of the island). There's a scenic stop that should be stopped at. Can get very windy and quite misty here.
In the east side, Kaneohe Bay, there's a nature park type things with mad plants - though i forget the name.
For nightlife there's quite a lot - you;d have to check when there. It does vary, though there's more on offer here than on all the other islands put together. There's karaoke, country/western, rave/techno, pop, soul/rnb, etc
Foodwise, if you don't like Asian cooking, you really don't belong here. There's Korean, Chinese, Japanese, Filipino, Thai, Polynesian, Hawaiian, Laotian.. the lot. And all sorts of hybrid recipes that are bound to happen when you melt that many races together. If you don't like that, there's steak houses, burger kings, diners, all night cafes and other Americana.
Oh and need i say - get a car (watch out for rush hour though!). Though the bus service here is the best on offer of all the islands, so you can survive without.
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