First of all, 2FA is a jolly good idea in terms of preventing account hijackings; relying on email/SMS (texts) introduces multiple hazards that can reverse 2FA's net benefit.

One configuration some people use is the KeePass desktop password manager, which supports storing TOTP seeds and has a nice UX for generating tokens; the password database file may be located as you see fit on a hard drive, DOK, cloud drive etc. Example of TOTP config for KeePass:

https://www.fhtino.it/docs/keepass-totp--intro/

Also, Keepass2Android can be used in similar vein from Android devices. iOS equivalents seem to exist as well.