Hawaii's daily paper is The Honolulu Advertiser. When we lived in Hawaii, I used to read this paper religiously - it is a great source of all things Hawaiian. The good news is now you can access it online, so I use their website as a way of keeping up to date with all the latest Hawaiian happenings. I have never been much of a fan of reading the daily paper, but I find that this paper is concise, factual and interesting. The Advertiser has some interesting lifestyle sections, and now the online version has some great blogs, including Urban Mix Plate, written by Melissa Chang - you can also follow her updates on Twitter.
Two sections of the paper that I want to call out are the My Advertiser section, which has user-generated content, so you can actually add your own news, stories or events in your local area. The other section that I find interesting is Island Life, which includes delicious recipes, travel info and fashion.
If you are planning a trip to the Islands, I would suggest subscribing to the Advertiser's RSS feed for a few weeks beforehand, so you can find out what's happening during your upcoming trip. You may find out that there is a festival of interest, some killer waves, or a new restaurant opening. Keep the Advertiser in your favorites - its a great Hawaiian resource.