Stay out of Kalihi, Waipahu (Kunia is ok), anything in between Kapolei and Haleiwa, and Waimanalo. As long as you're not a d!ckhe@d, you'll be fine, but there are folks there who don't take kindly to haoles (foreigners); and they tend to have the most gangs and highest crime. North Shore is ok--especially if you're a surfer and/or hippie. Kailua and Kane'ohe (and the smaller areas around them) are close to the Marine base, so you'll see a bunch of jarheads all the time. Ai'ea, Pearl City, and parts of Honolulu are nice. I knew a lot of guys who lived in or around Waikiki. If you like the night-life, that's the place to be. Ewa Beach is one of the less-expensive places, as well as Kapolei. Ewa has its own little slice of shadyville, though. Wahiawa is close to the main Army base; so if you end up there, you'll run into a lot of soldiers. Mililani is a nice area. It's not too expensive, but it's pretty well kept too. The east side is pretty expensive, and there's only one road in and out, so there's a lot of traffic somewhat often. If you can afford it, you can always try Hawai'i Kai or Kahala. They are the more expensive areas, but they're close to the public range. ;) For sake of disclosure, I'm not from there, but my wife is; and I lived there for 10 years (just left this past August). I lived in Kane'ohe (on base), Ewa Beach, and Ai'ea, and I like all of them.
If you have any other questions, I'd be happy to help as much as I can.