Nobodies mentioned car stuff yet so...
- Central Circuit is on the way to Hiroshima from Osaka in Hyogo Prefecture, but it's off the main travel route (most circuits are) so a train and a bus trip might be required depending on where you're coming from. Also depending on the actual days you're here, theres always some motorsports action going on. It's about an hour out of Osaka by car, easily add another 45mins to an hour on top of that if your going by train/bus.
- TI Circuit in Okayama prefecture is another good circuit but harder to get to. I can see only a 'Super F3' race being held there in June so... only go if you're really into open wheel racing I suppose.
- SuperAutobacs 43 Doui in Amagasaki is a SuperAutobacs 'complex' which is not just a stand alone store, but mixed in with many Restaurants and 'Autobacs C@rs Show', basically a custom car showroom, selling many cars from Tommy Kaira, Mooncraft, VEMAC... just go there it's worth the visit... even the car park and SuperAB garage area always has some sweet cars in it.
- Hankyu Sanbangai is not specifically a car orientated area, it's the shopping mall connected to Hankyu Umeda Station in Umeda, Osaka. You would have to spend a day or two investigating this place anyway (with Hep 5 Navio across the street, where the big red ferris wheel is), but if you're there on a Friday or Saturday night, you can see all manner of modified cars ranging from crazy Vans to European sportscars just doing laps around the block. I haven't been there in a while so things may have changed a bit, but around 8 - 9pm there should be something there.
Sorry the maps are in Japanese, just print them out and ask at hotel front desk/Info counter at station how to get there. This is also Osaka-centric, so others might have more info on other places around Kyoto or Hiroshima.