On a map, Nice and Monaco seem not too far from Grenoble but actually they are ! It's going to take you at least 4-5 hours either by train or car. The more direct road, although nicely surrounded by mountains, is a real pain.

If I were you then, I would stay in the Grenoble area. Why not week-ending in Lyon, which is famous for being the capital of typical french food and is one of the cities awarded by the UNESCO, or even Geneva or Annecy (nice lake as well and more reasonable prices). Those cities are about one hour away from Grenoble (train or car). I guess you'll be coming through LYS, so Lyon might be a wise and interesting choice (brand new Hilton close to the city center).

Whatever your choice, take a look at : www.viamichelin.com to find nice hotels and restaurants (the michelin guide is very famous in France, as you might already know, and can be trusted : some restaurants never recover after loosing a star in this guide).

Please don't hesitate to send me a mail since it's somewhat offtopic here ! (I'm a french student in Grenoble).