Check out Keepass! Rather than syncing directly into a Cloud, it allows you to store a database file into any location. It supports MFA (e.g. by combining a password with a secret file, or a Yubikey). And everything is open-source.
I like the model a lot, because it solves the "database ownership" issue, where your Password provider (be it LastPass, 1Password, etc) becomes in itself a weak link.