Well if you have to mess around with a broken bolt, that's a good spot.
If you go the center punch and drill route, grind the end of the bolt flat before you center punch. This will help you immensely in getting it punched and drilled properly. And really take your time to ensure you punch it in the center. When you drill make sure you are drilling straight through the bolt and drill it all the way through.
Once you get it drilled all the way through shoot some good penetrating oil in the hole and give it some time to work. Use the largest extractor you can and be gentle.
If it doesn't want to come out, and you drilled it really close to center and fairly straight, you can drill it incrementally larger and stop before you get into the thread in the head.
At that point you can carefully chase out what's left with a tap.
If it was mine I would pull the radiator for more room.