Monte-Carlo, and the rest of Monaco, is probably too expensive for the average backpacker. However, it is possible to make this a budget-friendly visit if you make it a day-trip from your stay in Nice or Cap-d'Ail in France. I explored Monaco by foot, enjoying a beautiful seaside stroll along the "Coastal Walk" from Cap-d'Ail to Monaco. The entire city-state of Monaco is very small, and I would say do-able in one full day, which you could extend into the evening to visit the Monte-Carlo Casino if you'd like.
Circuit de Monaco
A street circuit that is used once a year to host the Formula One Monaco Grand Prix.
Monte Carlo Casino
The Casino de Monte-Carlo includes a casino, the Grand Théâtre de Monte Carlo, and the office of Les Ballets de Monte Carlo. I'm not really a fan of casinos at all, but it this is a beautiful building. We weren't allowed to take photos inside, but here are a few from the outside. Monte-Carlo is definitely more of a luxury-destination (not my typical style of travel), but I would recommend it as a good day trip if you are in the south east of France.