Have you tried converting the zip codes to custom territories and using those on your map?
You should be able to define a territory using each of the dimensions that define the way that the zip codes are aggregated to territories.
Sarah, Thanks for your response. I tried this option and it works when zip codes come under one territory only. I am trying to create territories which may have common zip codes (overlapping with each other). I am really appreciating your help.
Would it work to just make four different sets of custom territories (one for each of your levels of aggregation - e.g., city, neighborhood, etc.) and then switch between them? You could create a hierarchy and the navigate up and down the hierarchy to see aggregation at different levels of geography.
Get Started Mapping with Tableau - look at step 4, create a geographic hierarchy