Skip Harbor Freight. Lowes might be worth a look but I wouldn't hold my breath.
On something like an extractor, you want the best you can buy. These things are notorious for breaking off and making matters worse. A cheap one will only bring you pain.
If there is some bolt sticking out, you can get something that looks like a regular socket but has a spiral wound set of teeth on the inside. Some people call them twist sockets. You need a full set to cover different sizes - you hammer them over the stripped stud/rounded bolt and they bight in as you turn them. They work as good as anything I've ever used in this situation.
If it's broken off flush, a left hand drill bit is a good start. Since this is a pretty big bolt you have half a chance - the small extractors almost never work. Be sure you center punch it exactly in the center, and work your way up from small to larger drill bits being careful to drill as close to the center as possible. If you can remove the carrier and use a drill press, so much the better but a hand drill will work with care. Drill progressively bigger until you get nearly to the threads. Then if it still hasn't come out from the left hand bit, you can use an extractor. I don't like the spiral kind for internal work like this, I prefer the square kind with a flute on each corner. Irwin makes some quite reasonably priced that you can often find at local hardware stores. Again, not great but given the size you have to deal with they should work.
Personally I've never had luck trying to weld a nut to a broken bolt but I've only tried a few times and I'm not a great welder anyway.
Here's a whole thread on the topic:
http://www.garagejournal.com/forum/showthread.php?t=95588