You have managed to find a remote place at the midpoint between Tokyo and Hiroshima. Great for cultural heritage. But I don't know if there are many recognizably named car places in that neighborhood.
KRS and Central Circuit are not too far from there.
Aquarius is close by, but their specialty is outside most people's interest.
DOME is around there somewhere too.
There should be plenty of tuning shops, and the size and impressiveness of the little shops never heard of overseas is close to the same as the names that are supposed to be impressive.
Invest in a rail pass, it will pay for itself quick, especially where you are going.
You may find yourself on your own if your friend works at a language school. That is supposed to be long hours and not much free time.
Don't worry much about safety. According to the natives, the only criminal element you will see is when you look into a mirror. They'll all be afraid of you, unless you bump into a bunch of English studying school children on a field trip. They will hound you with questions their English teacher assigned them to ask any foreigner they see on their field trip.
If you're loose in Kyoto or around Nara, you're going to be bumping into a lot of school field trip groups.