I must be odd. I love solo exploring (I think I got the bug while growing up - the adults in my life didn't go anywhere. If I wanted to see something, I had to find it on my own).
That being said, have the family you are staying with write a note for you that says "I'm lost and don't speak Japanese" along with the city/train station and line where they live. That way, if you get lost, you can whip out the note and someone will direct you in the right direction. I have a pretty good sense of direction, so navagating Tokyo was no problem. My relatives would freak out when I wanted to go somewhere on my own. You can not get lost on the trains.
Relating to what Pickles said, go and find what interests you. Don't be afraid to venture out on your own - you'll find the true sense of the people in back alleys and in small towns.
Don't let your anxieties get the best of your trip. Go out, explore and have fun. If you get lost, so what? You may make some new friends.