Compare 2 lists and return value

I'm working on generating an accurate list of Cities and Zip Codes within a given state (plus additional data). I have 2 separate lists where one contains more of the desired data but no zip codes and the other list contains no desired data except for the zip codes. Obviously i'd like to use the more detailed list but i still need the zip codes. I've pasted both lists in one workbook but on 2 separate sheets. The first problem i'm running in to is that the list of Cities i have is more comprehensive (2764 cities) than the list of cities with zip codes (1036 Zip Codes 814 Cities - some duplicates per zip code). i would like to compare the 2 lists and if a city name from the list i have is located on the second list, return the associated zip code. the format my data is in looks like this.

My City New City New Zip
Sheet2!F2 Sheet3!A2 Sheet3!B2

Any suggestions on how to accomplish this would be greatly appreciated
Thank you!