Does the monero wallet keep track of where I sent my coins to? Say someone found all my private keys for my monero wallet. Can they open the wallet and see where I've been spending my coins? This is assuming they have a profile of these addresses I sent to already.
The wallet cache stores the metadata of outgoing transactions (destination address, secret transaction key, transaction note), which is not stored in the blockchain (see also What data do the wallet files contain? for a list of what else is in the wallet cache file).
To have access to these informations, an attacker would need to get the wallet cache file and its password.
If the attacker only gets the private spend key or mnemonic seed, he will have access to the funds in the wallet, but he won't be able to recover the addresses where the wallet sent transactions to in the past.