The first thing you need to understand is that cryptocurrencies like bitcoin are the real money. They are not merely a measure of government fiat currency denoted in a different unit. With that in mind, your question doesn't make a lot of sense. It's like asking where the real money is stored when you purchase gold. The gold is the value. You have simply traded some other currency in exchange for it.
Exchanges, web wallets, and other "cloud banks" (although I've never seen this term) are just services that store your bitcoin for you. They manage your transactions, and often your private keys, so that you don't have to run software on a computer to do so. If you have given them US dollars, what you have done is purchased bitcoin with those dollars. This is just like purchasing a bag of groceries with your USD. Someone isn't storing the money you spent as a backing for the value of your bag of groceries in your pantry. You've simply exchanged one thing for another.