I've lived in Hawaii for 11 years now, all on Oahu. I've traveled to Maui and the Big Isle several times each and Kauai once. Each island has its own uniqueness and beauty to offer--and I refuse to claim that any one is better than the other; it all depends on what you are looking for.
If you are not sure what you are looking for and just want to visit then I recommend Oahu. Oahu has many secluded and beautiful spots as well as tourist spots like Pearl Harbor, Waikiki, North Shore, Punchbowl, Diamond Head, plantations, the Polynesian Cultural Center, waterfalls, Hanauma Bay, world class golf courses and hiking trails. There are plenty of national chain restaurants to make you feel at home or if you like hundreds of small restaurants catering to any taste. To top it all off we have the only royal palace on American soil.
If you are looking for a strictly nature experience than Kauai or the Big Island are your best bets. Kauai has the “Grand Canyon of the Pacific” and the Kalalau Trail along the Na Pali Coast to. The Big Isle has the only active volcano in the US, world-renowned observatories atop Mauna Kea, black sand beaches, the southernmost point in the United States, and some of the most amazing coastline you will ever see.
Maui is in the middle right now; there are many nice hotels/resorts and restaurants. Lots of things for visitors to do like fishing, diving, para-sailing, and snorkeling but still has a quaint feel to it. You can also do sunrise hikes or extreme downhill biking on Haleakla or drive the Road to Hana.
One thing you need to keep in mind when traveling to Hawaii is that it is different here. The people that don’t understand and respect that are the ones that have bad experiences. Life moves at a slower pace, if you smile at someone they will smile back, the beach is a lifestyle, and family is extremely important. Everything here isn’t rosy: we have traffic congestion, crime, an antiquated power grid, a large homeless population; our public education is in the bottom 10% of the country, and high taxes. It’s a small price to pay for everything else Hawaii has to offer.
…and as a bonus, all your dollars are being reinvested in America.