Hi don Jaime!
The flea market is on Sundays and Wednesdays. I get the feeling the better one is the Sunday one. No particular reason behind that, just a feeling.
KKB mentioned McD’s plate lunches. Despite my disdain for McDs (former employee here) and my reservations about plate lunches from a fast-food place, they’re not bad. (Rainbow’s, L&L, and even Zippy’s are still a billion times better.) Anyway, there’s three to choose from: chicken katsu, hamburger steak, and a fried fish plate. They’re all made with McIngredients (McChicken, Quarter Pounder, and Filet-O-Fish patties, respectively) and come with rice and macaroni salad. The rice is pretty decent for McDs-- it’s not igloo rice (hard on the outside, soft on the inside 
).
I don’t know about Aoki’s, but the Shirokiya in Pearlridge is no more. They closed up sometime in February or March (I was in CA at the time, so I’m not sure exactly when it happened). The Ala Moana one is still open, and IIRC will remain open. That one’s got the best chance of surviving anyway, I think, what with all the Japanese tourists and more serious shoppers there. But yeah, I was sad to hear they were closing, too. I didn’t realize that my last trip to the Pearlridge one would indeed be my last trip there.
Speaking of Ala Moana, they’re mostly finished with a very extensive renovation/expansion. If you haven’t been there in ten years, you won’t recognize the place. Neiman Marcus is there, as are a whole bunch of hoity-toity pricey places, like Gucci, Chanel, Georg Jensen (snicker), Tiffany… I’m forgetting quite a few, I bet. Eddie Bauer and Old Navy are also there now (finally).
Hmm, let me think… oh, there’s the (relatively) new Hawaiian Waters Adventure Park. It’s in Kapolei, which is kind of a long drive from Honolulu. Well, long by Hawaii standards–45 minutes to an hour, depending on traffic. I’ve never been to the park, but it looks like a lot of fun.
I second stopping by Liliha Bakery and having a cocoa puff. Heck, anything from that place is great. The butter rolls, for example. I used to have butter rolls for breakfast from there on Sundays when I was a little kid. (We lived literally across the street from there. If you do go, look across the street from the entrance at the fire station there; we lived in the yellow two-story apartment building to the left of it.) It might be out of your way if you’re going to be staying in a Waikiki hotel, but you could make it the first stop of the morning on your way to the mall or wherever you plan on going.
Of course, if you do go to Rainbow’s in Kapuhulu, you could always have a heart-stopping malasada from Leonard’s instead. Or better yet, you could take your plate lunch and malasada and take them to the nearby Karaoke Hut and sing the afternoon away. 
Kailua Beach is my favourite beach in Hawaii. Waikiki and Ala Moana are beautiful, but the sand at Kailua is cleaner and softer on your feet. There’s some shady spots perfect for setting up your mat and cooler. It’s far from the traffic, grime, and noise of Honolulu and Waikiki, so it’s nice and quiet there.
If I think of anything else, I’ll let you know. Oh, and my long-standing offer to ship Hawaii information/activities brochures and coupon booklets to any Doper who wants 'em still stands.
