Keepass has been my go to since forever, highly recommend. I never jumped on the SaaS password manager train when they started coming out, always just kept it local. There were times I thought I was missing out on some convenience but I'm glad I never moved.
Depending on your threat model, you can even just keep the .kdbx in cloud storage somewhere and point your keepass client to that. I'd recommend using a keyfile in addition to your master password though so that if anyone does happen to get a hold of the database they can't just make brute force attempts against it.
I’ve found being able to share passwords with my spouse very valuable which we couldn’t easily do with keepass. Also the syncing strategy on iOS is a disaster and corrupted my wife’s keepass db causing her to lose everything.
Is there reasonably priced cloud storage for this use-case? Their offerings are usually for several gigs of data, a kdbx is minuscule