INSERT INTO table (ID,City,Color)
SELECT ID, Moscow, Green
FROM users WHERE users.Name="Test"
INSERT INTO `table` (`ID`, `City`, `Color`)
SELECT `ID`, `City`, `Color`
FROM `users` WHERE `Name` = "Test"
// или если id не надо
INSERT INTO `table` (`ID`, `City`, `Color`)
SELECT null, `City`, `Color`
FROM `users` WHERE `Name` = "Test"