L.,
I have had some experience with all three places! I lived in Korea for 2 years, Visited Guam for 30 days and have visited Hawaii on 3 occasions for 1 week at a time. I also have friends who live in Hawaii and on Guam.
Here in a nutshell is what I know about each...
Guam - Small island not very close to anything, but easy to take trips anywhere on that side of the world! Getting involved with the spouses club there will give you the opportunity to go on the buying trips for the spouses gift shop. Once you have been everywhere it is easy to take your family and kids for your own private trips. Scuba Diving is awesome! Although the junior programs only will include your 12 year old, there is no better/cheaper place to learn! Snorkling is good at times, in certain places. Guam is considered an island getaway for the Japanese, so you will always see tourists while you are there, but there is a lot of rich history from Both WWI and WWII, as well as Native sites to see! There are snakes, mosquitoes, giant spiders and cool jungles on the Island. It is very humid all year round, be careful your A/C doesn't go out for too long, or you will have mold problems! Bring a car you don't mind getting rid of after your tour! Do Not purchase a Brand New Car before going here; Expect your cars to have rust, the Salty Sea Air will get everything!. Oh and develope your childrens swimming abilities, and ALWAYS obey the posted swiming limitations. BUY sturdy hiking boots before leaving for here as you will need them when getting around in the jungle/rocky areas while hiking! The BX and Commissary aren't fabulous, but they aren't severely limited either. Although cooking gourmet meals with exotic spices/ingredients may be out, depending on where the spices come from. While there I purchased one of Bobby Flays cook books and was able to make anything and everything in it. THE NEX on one side of the island has more stuff than the BX does.
Hawaii - Wonderful set of islands that have gobs of Natural Wonders... volcanoes, snow, beaches, monstrous waves; Beautiful sites to see ... Memorials, black sand beaches, Whales, Dolphins, Surfing Contests, and rich culture to learn. However if you are Caucasian be aware that you are not welcome in all areas of the islands, If you want to expereince a little racism, come here. IT is by no means prevalent or everywhere, but be aware of it, and be cautious. Should your kids for any reason attend off post schools, they will exerience it. Hawaii also has historical significance, but it is not near as easy to travel, and frankly a lot more expensive than Guam. Snorkling and Scuba Diving is Great, but more expensive. If you like authentic China Town, have no fear you will find places where the locals don't speak English. In the "winter" look for it to rain for part of the day every day, then be sunny in the afternoon. Again, you need hiking boots, but you are more likely to be able to find a good pair while you are here. Your local NEX and Navy Commissary is where you will find anything and everything under the sun! They are both monstrous as well as having their own giant/georgous complex!
Korea - If you love to shop and want to haggle over the price and buy cheap, COME HERE! I remember one such event where the only way we had to communicate was with a calculator! Depending on where you live in Korea, you may be able to catch hops out of your back door to all over the place. Korea of course is part of the "mainland" and so closer to other countries (the only reason I say this is I really don't like long plane rides). DEFINITELY GO to the DMZ while you are here. It is a solemn occasion and place, the North Koreans are always watching for propaganda they can use against the South and the US, but you will be briefed on that. I didn't get introduced into much of the Korean History, but the Culture is awe inspiring, and the old palaces are breathtaking. Please don't get to squeamish about their diets, and try some of the local foods, just ask first! There is a rainy season where it is horribly rainy for about a month/two (with off times of course), but this is the only spot where you will get all 4 seasons. Oh and be aware, I am not really sure what the smell came from but, I still remember the smell. You do get used to it, and will forget it is even there, but it may take a few weeks. This was in 1988, but the sanitation then wasn't top notch. I remember the BX being OK, not big, but not tiny, and the Commissary was really large, but this was also in 88 at Seoul.
Just know there is good and bad about each spot, but as you already know, A tour is what you make of it! Good Luck!
W.
Look up www.geocaching.com and with a handheld GPS you can learn/see so much!