Getting to Okinawa is usually accomplished by air from either KIX in Osaka or Tokyo Haneda airports. Be sure to get the Yokoso Welcome to Japan Fare from either JAL or ANA. (There are ferries from the main island, but they are fairly long trips.
On the main island of Okinawa, Naha up to Kadena on the west coast are pretty well westernized with a few exceptions such as Shuri Castle.
North of Nago is the Churaumi Ocean Expo Park with its huge aquarium with whale sharks, manta rays, and hundreds of other fish. There is also a dolphin show that is very fun especially for young kids.
http://www.okinawaindex.com/index/?tid=3&cid=65&id=17and
http://www.kaiyouhaku.com/en/index.htmlAlso near Nago is NEO Park which is an open air zoo.
http://www.okinawaindex.com/index/?tid=3&cid=65&id=19and Okinawa Fruitland.
http://www.okinawaindex.com/index/?tid=3&cid=65&id=22Ryukyu Mura between Nago and Kadena would also be interesting as it is a depiction of an ancient Okinawan village. See
http://www.okinawaindex.com/index/?tid=3&cid=65&id=25and
http://www.ryukyumura.co.jp/pdf/e_001080124.pdfThe village website is in Japanese.
There is also Murasake Mura which is also a replica of an old Okinawan village and has activities in which the kids can participate.
http://www.okinawaindex.com/index/?tid=3&cid=65&id=12In the southern part of the island is Okinawa World with a large cave you can walk through (I highly recommend this) and many exhibits on Okinawan culture. I particularly enjoyed the young kids doing a dance and the Taiko drummers. There are also Eisa dancers/drummers and a large shisa (liondog) dance. The kids might also enjoy the habu museum if they find an interest in snakes.
http://www.okinawaindex.com/index/?tid=3&cid=65&id=3Another fun thing to do would be to take the ferry from Naha port to Tokashiki Island about 20 miles west of the main island. This island is definitely Okinawan. If you decide to go, take a bus from the Tokashika port to Aharen beach. There is a small village there. The beach is fantastic and I would definitely get the kids some snorkeling equipment and let them cruise around in the enclosed area of the beach and see the fantastic array of tropical fish (nothing scary). However, the butterfly fish may swarm around you. There is also a yellow submarine with a glass bottom (it doesn't actually submerge) at the port near Aharen that will take you on a cruise around the bay. We saw a sea turtle when we went. This island was one of my favorite places in Japan. There are several dive shops in Aharen that will rent you snorkeling gear and show you how to use it. Look at the marine activities section in the photo gallery at the website below.
http://www.vill.tokashiki.okinawa.jp/en/lets_go/ett.htmWhile on the island of Okinawa, I would recommend renting a car to get around. Most have GPS units and although they are in Japanese, you can find your way around easily. (They also show where all the convenience stores are. They have clean western style restrooms.) You will need an international driving permit and they drive on the left side of the road as in England.
April or early May before the rains start is a good time to go, although you may have to deal with Golden Week, a national holiday. We went there over Christmas the first time. Nice, but not recommended as the water is too cold. The second time we went in early October. The weather was still quite warm, no all day rain, the ocean was quite comfortable, and not much in the way of crowds.