You're in luck...most places are very friendly to our 18+ crowd.
Where do I start?
I suppose it depends on what kind of crowd you'll want to hang with. As with any club/bar in Waikiki, if you want to hang out with tourists and other non-locals, your best bet would be Zanzabar, located in the Waikiki Trade Center. They have Thirsty Thursdays (18+). I am unsure if Friday and Saturdays are (21+), but you can always call ahead. (Open till 4AM)
Blue Tropix (across the Convention Center). All their nights are 21+. AFAIK, their Wednesday, Friday, and Saturdays are their busy nights. It's a mixed crowd...you'll get some locals, some military, some tourists. (Open till 2AM)
Then my favorite--Pipeline Cafe (located about a qtr of a mile from Ala Moana going West), it's just a short drive/cab ride from Waikiki. It's in kind of an industrial area so it's kinda tricky giving directions. They just renovated it, so it's even bigger now, and it's the largest club on the island, IMO. It's 21+ for Dollar Drink Tuesdays, but on Friday and Saturday it's 18+. (Open till 4AM)
There are a bunch more, but those above are the ones that are actually worth going to that aren't awful and cheesy. If you're interested in 21+ clubs just because I can elaborate on those too.
If you're going to be in Waikiki, may I suggest Duke's Restaurant for awesome awesome fish and prime rib (they also have a kick ass buffet)? There's also Kincaid's at the Ward Warehouse, Kua`aina Burgers on Kalakaua Ave, Assagio's (Italian) at the Ala Moana, Angelo Pietro (Italian/Japanese) on Kapiolani, and Ryan's Grill at the Ward Centre.
PM me if you have any more questions! Hope this helped!