I use gmail for my online adventures in a separate browser with privacy mode on.  I have never associated that gmail with a phone or other address and that seems to be becoming a problem.  When I travel out of town and use my laptop, I get blocked from that gmail account.  When I return, I get a message that "someone" has my password and access was blocked.  This was determined by IP address.   I check the box stating that it was me and assume everything will be okay next time. (it's not)  I would like to use backup codes or some non personally identifiable method to connect (or enable that laptop) when traveling, but it seems like google is headed in a direction that is not compatible with that. (must have phone or backup email)
I like gmail because it keeps my stuff together and, if I croak, the account should be permanently lost with no way for someone to discover it short of hacking it.

Has anyone got a suggestion for a more secure way to do this that doesn't require frequent access to maintain?  

Thanks