I just moved into a house that has Nest temperature controllers in both the upstairs and downstairs. I don't plan to have any wifi in the home and I want to replace Nest with hvac controllers that have no wifi. I see that the Nest's are easily unplugged from their socket. Do all hvac controllers plug right into that same socket or was that wired specifically for Nest?
The "socket" or mounting plate goes with the thermostat, and a different one will come with your new thermostat.
Be sure to keep the plate with the Nests when you put them up for sale. Those should more than pay for replacements, even brand-new ones. If you are willing to buy used thermostats, those are frequently quite inexpensive since lots of folks took out perfectly good ones to install "smart" thermostats.
Do not disconnect the current plate without first documenting exactly which wires go where. As a rule, it should be easy to retrofit a "dumb" thermostat, since they will not use any more wires (and often fewer) than a "smart" or "wifi" one.
So, in summary: to remove the Nests from the home, you need to get replacement thermostats, document the wiring of the Nests, transfer the wiring to the same terminals on the replacement thermostat mounting plates, and install the replacement thermostats. If you find that you have an "extra" wire with no place on the new thermostat, insulate it (so it cannot make inadvertent contact with any other wires) and leave it behind the wall for future use.