What is the equivalent of 555 for postal addresses?

I'm not aware of any "fake" zip codes that are commonly used in movies. However, some digging has suggested that fake zip codes are probably not required.

Firstly, zip code is a five digit code. According to Carrier Routes there are approximately 43,000 zip codes in use in the US. As a five digit number can go up to 99,999, this means that over half the "possible" zip codes created using five digits are not in use.

Now, according to this site, zip codes work in the following way:

The digits mean specific things and here is what they mean:

The First Five Digits

First Digit: A broad geographic location.
Second and Third Digits: Pinpoints a more specific area.
Fourth and Fifth Digits: Designates Post Offices and/or Postal Zones

In 1983 an expansion was needed and became known as ZIP+4. This meant better and faster deliverability for our mail. The 4-digit add-on identifies the following:

City Blocks
Office Buildings
High Volume Mail Receivers

So it seems likely that film creators, if they really wanted to, could examine the codes for a particular area and ensure they chose a "fake" one, i.e. a code that wouldn't work in a region.

Furthermore though, a zip code is simply used to get mail to the right area. Once there, the local address is used to actually get it to the right house. Even if a real zip code was used, if it didn't match the right address for that zip code in anyway, it would be returned to the sender (or whatever the policy for US postal companies is).

Finally, I would argue it's not as necessary to fake zip codes. When a phone number appears on screen, it's easy to try it out. You dial the number and in real-time can get in touch/hear/listen to someone. A fake zip code requires the hassle of creating some sort of letter/parcel, posting it and then waiting for the other person to be nice enough to reply - which if the address was featured on television is extremely unlikely! Therefore, not only does it take a lot more work to get in touch with a zip code seen on television, the likelihood of a response, when compared with phoning someone, is much, much slimmer.