I've hunted caribou in Alaska, Northwest Territories, and Quebec and had good and not so good hunts in all three places...
For a first time hunt, I would recommend booking with a reputable outfitter in Quebec..No hunt is a sure thing, but your odds are probably the best of having a successful hunt and a quality wilderness experience there..
I've used Jack Hume Adventures
www.jackhumeadventures.com and would highly recommend them..I've also heard lots of good things about Tuttilick ( sp.?) but have never hunted with them... Hume is honest and very well organized, has lots of camps to move hunters around to, and has the personnel and the resources ( airplanes) to do it... I'm booked to hunt with Hume again next September...