1.) Car - I normally would say it's optional, but because it sounds like you a travelling with little ones, you might need one to store the car seats/strollers. I am assuming (and hoping) you'll want to do a bit of sightseeing and go out of Waikiki. Just remember, Honolulu has an excellent mass transit system, TheBus that has stops convenient to the HHV. Might work for short trips. Parking can be a challenge in Waikiki.

www.thebus.org

2.) Good rates for car rentals - perhaps a Priceline bid?

www.biddingfortravel.com

3. Cheap stores - In the HHV and about every other coconut tree in Waikiki is an ABC Store. There are also many shops in the HHV and in Waikiki; a large concentration are in the International Marketplace. Ala Moana Center also has nice stores. The Costco by Salt Lake is closed. If you do a "Costco" search on this topic, you wil find a recent discussion on the various Costco locations.

4. Restaurants that are kid-friendly. I'll have to think on this, but the Wailana Coffee House across the street from the HHV is a good option for relatively inexpensive meals...

Hope this helps...