Moscow is certainly one of the world’s great cities from a historical standpoint, but for tourists it’s still largely undiscovered. Now that Western visitors are welcome the infrastructure is building, though it can still be a frustrating place to go.
Another difficulty the city has is that Moscow is very expensive, even by most European standards. Hotels in the lower categories can be affordable, but standards tend to be equally low. Once you get into the nicer business hotels the prices skyrocket to among the most expensive hotels on earth. There are a handful of hostels in Moscow, which are also expensive compared to other hostels, though at least cheaper than Moscow hotels.
Once you are in the city you’ll find that transportation is cheap, and most of the main attractions are quite affordable as well.
Food and drinks can be a problem for budget travelers since places with English-language menus are typically incredibly expensive. You can actually eat and drink well in Moscow for a reasonable price if you can navigate the restaurants and watering holes where the locals eat and drink.