Eliminating rows in a dataframe based on specific conditions
This snippet should do the work: 

city = ['PHX', 'JFK', 'NTU'] 
colomn_to_exclude = df.apply(lambda row: (row['origin'] not in city) and (row['destination'] not in city))
new_df = df[~colomn_to_exclude]


the second line checks the lines where your exclusion condition is verified and the line after subset the dataframe accordingly. 

You could also write something like 

colomn_to_exclude = df.apply(lambda row: (row['origin'] not in city) and   (row['destination'] not in city))
df.drop(~colomn_to_exclude, axis=1, inplace=True)


and you won't have to make a copy of your dataframe