There is occasionally trouble at the parades, but not much more than you'd get whenever you have a group of people out on the streets 'celebrating' and some alcohol thrown in. If you have a rough idea of where you're going to be on which days you can check them out on the Parades Commission website
here - though the roads will generally be closed a couple of hours before the parade starts anyway so you're unlikely to drive into the middle of one. If you want to see one the one in the centre of Belfast is really impressive, and better organised than some of the smaller ones.
I was up at the weekend with my C-reg and was grand, aside from the few kids that pointed as if to say 'oh look, they're lost'

That said I wouldn't leave my car parked on a street in the immediate vicinity of a parade, in case someone gets a notion for trouble and your car is different to all the others because of where it's from. It's unlikely anything would happen, but better to be safe than sorry.