I'm trying to send a letter without anyone being able to see where it came from. I know a letter can be sent without the return address, but it is usually still stamped by the post office with the city and zip code. Is there any way around this?

Hmmm... if you don't want to identify where you're living, you could try this: Send your sealed, addressed letter inside another envelope, and send it to a friend or acquaintance who lives in another state/country. Have that friend post your pre-addressed letter for you. The recipient will see where the letter was mailed from, but it won't identify where you're living.

Or send it from a completely different post office

And if you really want to be secretive, send it to an accomplice in an entirely different part of the country (in a second envelope, of course) and have THEM pop it into a post office drop box. ;)

You can send your letter in a stamped, sealed, addressed envelope to another post office. They will open the outside envelope and mail the one inside of it. You can do this anywhere in the U.S.
It will be postal stamped at the second post office.

Wow, the things I learn here. :)

Who knew? Here's another option. http://www.sendanonymoussnailmail.com/faqs/