What are the best souvenirs from Hawaii ?

You got some good suggestions here. You might also want to consider kukui nut necklaces. They were really in style a few years ago in L.A. -- Nicole Richie and Jessica Simpson were wearing them and everyone thought they were hot for a short time. I still wear mine on Aloha Fridays at work. I got a pretty one with different colored hibiscus painted on each nut.

Take an extra bag (like a soft duffel) with you when you go to Hawaii. Fold it up small and put it in your luggage. Then you will have room to bring home all your coffee, mac nuts, etc. Make sure you check with your airline first to find out the bag restrictions, including weight. Some people find it easier to just ship their souvenirs home the day before they leave the island(s). If you can get everything into a couple of Flat Rate boxes at the post office, it won't cost you more than $20. Much better than paying an extra baggage charge at the airport.

It could be anything really. There is many souvenir shops in Hawaii to accommodate tourists. You can find hats, shirts, coffee mugs anything you want.

For yourself or someone else?
For myself I'd get a t-shirt.
For others a freshwater pearl necklace or bracelet, fresh pineapples, kona coffee, or chocolate covered mac nuts are all sure to be a hit!

Go into any ABC store and you will find everything you need. Puka shell necklaces, t shirts, candy,Kona coffee, you name it and they got it.

Walmart has a huge souvenir section and not bad prices. Also a must have are macadamia nuts, Kona coffee, and local made cookies which come in all flavors. Jams and jellies are also great to gifts. As for yourself a beach towel or even pot handles. Which by the way all are at Walmart. Stay away from paying too much at the ABC stores.

If you are in Hilo on a Wednesday or Saturday, the Farmers' Market downtown is huge and really fun, with a great variety of gift items and handmade things, also coffee, nuts, cookies, etc. The stores in the National Parks and museums have beautiful, locally made gifts too.

It is really easy to find things you will want to buy. Finding room to pack it to bring home is harder.