I also live here on Oahu. I have the 10-22, 17-55, 24-105 and 70-200. 90% of time time I have my 17-55 on my camera. Mostly because it is the most versatile lens in my arsenal. It covers a very useable focal range, and has awesome low light capabilities (being a family vacation, you'll also be having dinners, and going to shows, etc).
If you opt for a little more focal range then i would suggest the 10-22 and 24-105 option, although, if you shoot like me, you'll find yourself changing up lenses quite often as I typically shoot in the 17-50mm range with some jaunts into UWA or Telephoto...
Can you list some of the activities you will be doing?
For me, when I do "touristy" things around the island, this is what I take:
General walkaround - 17-55
Zoo - 70-200
Beach/surf shots - 17-55 & 70-200 (sometimes 10-22, depends on the beach)
Hiking - 17-55
Luau Show - 17-55 & 70-200
Museums - 10-22 & 17-55
Downtown/China Town Walk - 17-55 70-200
So my vote is for the 17-55 (maybe supplement with a 55-250?) Hope this helps, and have fun on your trip...
5D MKIII|7D w/ Grip|EF-S 10-22MM f/3.5-4.5|EF-S 17-55MM f/2.8 IS|EF 24-105MM f/4L IS|EF 50MM f/1.4|EF 70-200MM f/2.8L IS|85mm f/1.8|35mm f/2 IS|70-300MM f/4-5.6 IS|580EX|Manfrotto 055PROB|2x PCB Einstein 640