Yes, invest 500 yen into Suica card (you can get the deposit back at the end of your trip if you want). Then load a few thousand yens into it, it will make traveling around the city MUCH more convenient.

I am currently in Japan on our family's second long trip here. We don't speak Japanese except the few most common phrases (which always seem to be apprecoated). I agree pretty much with everything that has been said in this thread so far.

1) You will be fine. If Japan is not the world's safest country, it ranks pretty high anyway.

2) Navigating the streets etc. takes some time getting used to, even though all the signs are also in English. Since Tokyo is a BIG city, the local transport system is also BIG. Well, make that HUGE. It is better to at least have a look at the maps beforehand. Also, plan your day(s). E.g., "This day we will do some shopping in Akihabara, including lunch." This will reduce the amount of time spent on trains. Also, avoid trains during the morning rush hours. Traveling at those hours is not pleasant, especially with children. Have a long breakfast, and head out around nine or so.