I've just recently set up my Nano S and wondering that when i send my Bitcoin to my Ledger live desktop app with my wallet connected
to the computer. does it go onto the ledger or are my keys on the computer.
Your coins are not actually stored on your ledger live application or on your hardware wallet, but they are stored on blockchain and hardware wallet is acting as device for signing your transactions and for storing seed words offline.
Point of hardware wallets is to keep everything offline as much as possible, so make sure your seed words never touch internet and never import them hot wallets, never send them anywhere online.
My suggestion when you are using Bitcoin is to connect Electrum wallet with your Ledger hardware wallet and use that instead of ledger live application, and for all other coins you can use ledger live.