IANA maintains many time zones in cities that represent the world. I don't want to maintain a list of all zones in a UI (because it's a third party system and would be unpractical to do so) and offer just the 4 main choices. Now which IANA value best represents these choices?
America/New_York
America/Chicago
America/Denver
America/Los_Angeles
I picked these cities to map for each zone. Are these appropriate choices?
Yes, I should say that the four IANA time zone IDs you mention are appropriate choices.
One way to see it is, inspect the list of time zones, link below. It lists the following time zones as deprecated:
I hope that you are aware that even though these four zones cover most of mainland USA (excluding Alaska), they do not cover all of it. One zone not covered is America/Phoenix, which, if I recall correctly, does not use summer time (DST) and therefore cannot be covered by any of the four main time zones. The list I have linked to contains 28 canonical time zone IDs in the US, so this is the minimum number you will need if you want to cover every square mile of USA.
Bonus info: The corresponding time zones for Canada would be America/Toronto, America/Winnipeg, America/Edmonton and America/Vancouver.
Link: List of tz database time zones on Wikipedia