Heck, even driving to any sufficiently large city rand(10,50) miles from where you live and putting the enveloppe in any random mailbox is pretty much guaranteed anonymity.
I would be wary of surveillance cams - they would know the thing was dropped in a box between x and y times, check the cameras and have a list of potentials. They could then go back and follow you after the fact to see where you went.
If you recall this is how they caught the guy who had a car bomb in his car near times square in NYC.
Much safer to either place in someone else's outbound mail in a deep and foreign-to-you residential neighborhood or, ideally drop into a mailmans box in his vehicle when he isn't looking.
For example, when a mailman parks in front of a multi-tennent mailbox on the street and he is standing within feet of his vehicle - they typically leave the rear door open, you could place it in at that time without being seen.
There are cameras on most suburban and rural mailboxes in the states? Here in Australia there are plenty of mailboxes where you likely wouldn't even be witnessed at all placing mail into.
There are cameras on anything that can accept packages over a certain size. Kinda stupid since the anthrax came in an envelope, but you know, anything to support the panopticon.
edit: I could be wrong about the above, I haven't found anything to support my assertion, though I am pretty sure I got that impression from the automated kiosks. They display a notification that packages over a certain size cannot be accepted without a camera. It's possible that a lot of rural POs don't have cameras though I'd be surprised if it were common.
You simply take the envelope to be mailed into a residential area and hand it to any mailman walking around.
There are no surveillance cameras, and the mailman isn't going to remember shit.