We stayed at the Chateau Beauregard in Jan. 2005. It is right in your price range. More of a B&B or pension than a hotel but we found it to be perfect. Just up the hill towards the ski lift to Le Brevent but easily within walking distance of the Aiguille du Midi cable car station. In fact, it has a gorgeous view of the Aiguille and Mont Blanc. Its website is: http://www.chalet-beauregard.com/rub1_en.html

Have fun in gorgeous Chamonix. John in San Diego