Where do all these hedge funds have their money? Not what investments, but who holds it for them?

Funds that trade their own account. I'm not talking about stocks, bonds or money market accounts, but which institutions hold their funds? Goldman Sachs, Morgan Stanley, etc? They have to go through a big brokerage firm anyways so is their account with Goldman who just charges them trading fees?

Do they hold their money with investment banks like Goldman Sachs or Morgan Stanley? Or do they hold it with the exchanges like NYSE? If I'm a fund manager and I have my assortment of investments and trade my own account, who holds my money? Do I have an account with a brokerage firm and within that account is my portfolio? If I trade my account on my computer, where is the money held? It's hard to believe that eTrade would let my hold $10b in cash in its account. Where is my stockpile of cash held? I know money markets, but specifically where?

Hedge funds have accounts at the primary dealers, the top investment banking firms, like Goldman and Morgan.
The NYSE is an exchange and does not hold investors money or accounts.
Most securities are held in electronic form (called book entry )at the Depository Trust Corporation (DTC). DTC is a corporation owned by all of the brokerage firms. By holding most of the issued securities in book entry form, DTC facilitates the settlement of trades between the brokers and their customers accounts, by recording the transactions on their books thus eliminating the need to transfer paper stock certificates.
Money held at a brokerage account is usually swept into either a related bank account or other money market account. Your brokerage account agreement will specify what it can do with your cash balances, especially if the cash amounts exceed FDIC insurance limits