Did it snap because it was too tight going in or did you just do the nut too tight ?
If you need to drill, ie not enough left to get hold of, just place rags around area to stop swarf getting places.
If there is enough to get a old nut over I would first try welding a nut on the remains, applying as much heat as you can get away with, as it will help.
Failing that drill and extractor needed, but nut and weld vastly better.
tabetha