The left hand side of the road thing isn't difficult to get used to at all. The two things I'd suggest you be careful of is which direction you should be looking when entering a road (ie look right instead of left) and believe it or not changing lanes on the freeway where you have to drive conciously, not sub-conciously.

I've hired cars i japan often and found it's a great way to get around when you're using them the way you have described (shinkansen/express train to the major town, car for exploring surrounding area). You can get sat nav on pretty much any rental car in japan but while it will be in japanese you can use phone numbers to enter locations or if you're with someone we've always used a map to see where we want to go and the sat nav to show where you are.

I've always used this website to organise rental cars in japan, super cheap and no hidden extras.