Get city name either do not start with vowels or do not end with vowels

SELECT DISTINCT city
FROM   station
WHERE  city REGEXP '^[^aeiouAEIOU]|[^aeiouAEIOU]$'

Assuming you are using MySQL, Here is what you are looking for

SELECT DISTINCT city FROM station WHERE city RLIKE '^[^aeiouAEIOU].*|.*[^AEIOUaeiou]$';

Footnote : RLIKE and DISTINCT

This SQL Query will helpful for you. If you are using MS SQL then follow this line of code given below:

SELECT DISTINCT CITY 
FROM STATION  
WHERE CITY NOT LIKE '[AEIOU]%' OR CITY NOT LIKE '%[aeiou]';

If you are using MySQL then follow this line of code given below:

SELECT DISTINCT CITY 
FROM STATION 
WHERE (CITY NOT IN (SELECT DISTINCT CITY FROM STATION WHERE CITY LIKE '%a' OR CITY LIKE '%e' OR CITY LIKE '%i' OR CITY LIKE '%o' OR CITY LIKE '%u'))
OR 
(CITY NOT IN (SELECT CITY FROM STATION WHERE CITY LIKE 'A%' OR CITY LIKE 'E%' OR CITY LIKE 'I%' OR CITY LIKE 'O%' OR CITY LIKE 'U%'));