Most visitors stay in Waikiki or Ko Olina. There's more to do in Waikiki, shopping and dining wise. Ko Olina is more quiet with less things to do. People staying in that area will have to drive to Ka Makana Alii, Waikele Outlets, or Pearlrige for the nearest dining and shopping options. Ala Moana is the biggest shopping mall on the island. You can find whatever you want there.
Most visitors like to hike Diamond Head or Makapuu Lighthouse, go snorkeling at Hanauma Bay, and visit the North Shore. Whenever I'm on the North Shore I like to go to Giovanni's for their garlic shrimp plate and Matsumoto's shaved ice.
Hawaii is a melting pot, so you'll find all kinds of cuisine here: Chinese, Japanese, Italian, Hawaiian, etc. I'm not sure what kinds of food you're into. I highly recommend giving Hawaiian food a try, since you can only get it here. Get a Hawaiian plate that consists of laulau, kalua pork, chicken long rice, lomilomi salmon, poke, and haupia. If you go to Ala Moana Makai Market food court you can find this at the Poi Bowl. Poi Bowl will have everything except the poke. For poke you'll have to walk down to Foodland, still at the mall. They have one of the best pokes around. Other places will be Young's Fishmarket, Yama's, and Highway Inn.