Well I ended up with a set of Cobalt drills but I have to tell you that these tend to be almost too brittle when drilling broken bolts. They tend to chip the points when they grab into the really hard stuff. They are the best drilling bit set I have used for drilling most anything however.
That being said. ---
One method I use for drilling out broken off bolts has been the use of "left handed drill bits", they usually bite in and spin the remainder of the bolt out. I usually pick up a couple of sets at Harbor Freight to throw in the tool box.
Another technique is to use a oxy-acetylene touch with small tip and heat the broken bolt until near cherry red and touch a wax candle to it. The hot bolt instantly melts the wax and is drawn into the thread area where it seems to really loosen the bolt.
I never really had great luck with the "easy-out" left hand spiral twist tools. I also picked up a set of those nut-like extractors which could grab onto a protruding broken off bolt but haven't had the chance to try them out much.
Just my 2 cents.
Bill