If you drill it, it has to be centered. Looks like the bolt it broken down in the hole. Use a largest drill bit that just fits into the hole, and drill just enough to make a shallow hole so a smaller bit will not walk. Use the proper size drill bit for the easy out and drill the rest of the way. I would suggest a left hand drill bit for this step. If the bolt still failed to come out now try the easy out. Use a hammer and lightly force it in, and try to extract the bolt. Probably did not come out, try to heat just the bolt and once hot, press a chunk of wax onto the bolt, let cool, try easy out, repeat may take a few times, be patient to not try to force it with the easy out. If this did not work now we procceed to why we were so careful centering the hole.
Find the appropriate drill bit for tap. If the hole is CENTERED AND STRAIGHT, most of the time the bolt can be drilled out even the threads will come out. The drill bit needs to be same size or bigger then the minor diameter of the threads on the bolt. Going up a 1/64" on the recommended drill size is not a bad idea. Done right, a bolt will screw right back in without chasing. Do not try to do this on the vehicle, it will make very difficult.
Welding a nut on is not a bad solution. It just makes the last resort of drilling out the bolt difficult.