1Password X is a Chrome extension, but it's also a full-featured 1Password client! Additionally, 1Password X does work without an internet connection. In version 1.5 we added an offline cache so you can boot up your laptop, unlock 1Password X and get that WiFi password or whatever item you need. If you haven't checked it out lately, I'd highly recommend taking a peek at this recent blog post: https://blog.agilebits.com/2018/03/13/1password-x-better-sma...
I just use KeePass and store the database with a cloud provider so I can access it from all of my devices. There are clients for all platforms, including mobile ones. Seems to work pretty well for me. Probably a bit more setup than 1Password, but I like having more control over it. You could even put a key file on a flash drive for a bit of physical security.
I'm sure 1Password takes security very seriously, but it seems like a big potential attack vector so I prefer a bit less obvious way to store my passwords.
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Jamie Phelps
Code Wrangler @ AgileBits