Eldman was a city located in a place that started with the letters "New..."
Gary Mitchell was born in Eldman on stardate 1087.7, and resided there at the street address of 8149. (TOS: "Where No Man Has Gone Before")
This information was listed on Mitchell's personnel file shown on Spock's viewer. It does not list what planet this city is located on.
A comparison with Elizabeth Dehner
's file, which appears to use the same basic format but of which a larger section was seen, would suggest that the "New..." referred to Eldman's state.