Some time ago you asked me for my advice: what were my "best tips" for a family with young children relocating to Tokyo? My boys were 5 and 7, around the same ages as yours, when we arrived at the tail end of 2007. So here's what I suggest:
1. Don't drive everywhere. Take advantage of Tokyo's superior mass transit system. Not just the Metro and JR trains, but the buses too. They're clean, safe, and reliable, and will take you virtually anywhere you want to go. Study the maps and play around with Hyperdia.com to figure out the different lines. (Apparently there is a Hyperdia by voice app now, and Hyperdia Lite for Android phones.)
The system is extensive, to be sure - you will be amazed at how many suggested routes Hyperdia will give you between the same two points - but in time you will learn the best ways to get yourself from here to there. Most importantly, you will feel more connected to your new city, and you'll gain a deeper appreciation for the local culture. There's nothing quite like emerging from Shibuya station on a glorious sunny day and crossing that big intersection, immersed in the colorful-yet-always courteous crowd, squeezing your kids' hands tight. It's a rush. You may think ohmigod what if I lose them in the crush but you won't because if you do get separated all they have to do is shout "MOM?!" and you will hear them, because here's the thing about Tokyo: the streets and sidewalks may be jam packed with people - the sardine can metaphor is appropriate above ground too - but they are also almost supernaturally quiet. Like somebody hit the mute button.
Bottom line is, time in the car is like time in a bubble. Which brings me to my next tip:
2. Don't dwell in the expat bubble! It's a trap many expats fall into, sometimes by default but often by choice. It's a missed opportunity. Don't make the Tokyo American Club your second home. Go to coffee morning - a great opportunity to pick the brains of those who've come before you - but don't lose whole mornings at Starbucks. Be adventurous. Leave the comfort zone. Make Japanese friends! Find one or two other curious, open-minded, ballsy people whose kids are also in school all day and plan day trips with them.
3. Try to learn Japanese. Even a few words are better than nothing (Hello, How are you?, See you later, etc.). Learn how to give directions to a taxi driver. (Turn right/left please, go straight, you can drop me off here, how much? Thanks). Learn how to order coffee and beer, and how to say Do you have an English menu? You may never be able to carry on a real conversation, but it's nice to be able to exchange a few pleasantries with folks.
4. Go skiing! We had a blast in Nozawa Onsen, Zao, Naspa Ski Garden, Hakuba 47, Happo-one...The Japanese ski instructors we encountered were very nice to our children and many can speak just enough English to get by. You can also hire native English-speaking instructors if you want to spend gobs more money. There are loads of Australian expert skiers about, and running their own lodges.
5. Network! This may be the most important advice I think I can give. Remember that you don't have to figure everything out on your own. Find like-minded expats who have been there longer than you (but not so long they've stopped appreciating how amazing Tokyo is) and ask them what they do and where they go for this, that and the other. Everybody knows at least somebody who's been there/done that.
Hope that helps. Good luck!
P.S. Here is a (partial) list of places I recommend that you take the kids at least once. I'm sure there's a blog post or two about each one, will someday link this list but for now I'll just type 'em out:
-Showa Kinen park (a day trip)
-Heiwa no mori obstacle course (bring change of clothes for when kids end up in the muddy pond, which they all do eventually)
-Children's Castle on Aoyama-dori (an hour or two after school, weekends it can get very crowded)
-Yoyogi park on a Sunday (particularly around the East Entrance near Harajuku station)
shrine (Sunday mornings for wedding processions, or during the
Shichi-Go-San celebration over one or two weekends in early November,
when 3- and 7-yr-old girls and 5-yr old boys go to the shrine for a
special blessing dressed in traditional formal attire)
-Tama Zoo - be sure to ride the lion bus!
-Toho Cinemas at Roppongi Hills (select your seat ahead of time, grab a beer with your popcorn)
Disney Sea (a day trip best taken on a weekday - this park gets less
crowded than Disney Land and is arguably better; nobody does Disney like
the Japanese. It's a date place for young sweethearts!)
-Nakameguro canal, in late March/early April when cherry blossoms are in full bloom
-Kamakura and the Big Buddha - a day trip and a hiking trail
-Restaurants: Korean barbecue, shabu-shabu, tonkatsu ramen, kaiten-sushi (a.k.a. sushi train)
bookstore in Shinjuku (adjacent to Tokyo Hands and Takashimaya- closer
to Yoyogi JR station but has big big "foreign books" floor where you'll
find lots of children's books (in English) and Japanese manga translated
into English, books, magazines, etc. Tower Record in Shibuya also has a
pretty good foreign books floor but seems more expensive)
-Odaiba (Sony ExploraMuseum, marine park, Statue of Liberty)
-a neko cafe (if you like cats; you can play with the "staff" while you have a cuppa tea)