Amazon makes it pretty simple even if you don't have an address. The hard part is know what town you'll be in the next few days.
Getting mail on the road isn't exactly rocket science. I'm a huge fan of Prime—seriously, who isn't—because of the free two-day shipping and I know exactly when the package is coming.
(It also helps Amazon is beginning to offer reduced same-day and one-day shipping. I've definitely taken advantage of that a few times when I have forgotten to buy a few things for a trip in advance.)
In the few instances when I haven't been able to send a package to a local friend, hostel, hotel or Airbnb, Amazon offers a couple of different options for picking up packages without inconveniencing anyone.
Amazon Locker
The first easy, under-publicized option is Amazon Locker, where the package is delivered to a specific spot until it's picked up.
During checkout, Amazon offers Amazon Locker as an option right below the shipping address. I found that Amazon Lockers don't seem to be present in every city but are at least available for major cities.
To check out whether there's a nearby location, I'd check here.
That doesn't mean the package will sit in an Amazon Locker indefinitely, though, so it's worth to plan the order in advance and err on timing everything just right. (I like to have it delivered a day before I arrive to be safe.)
The site clarifies:
Once your package is delivered to the Amazon Locker, you'll receive an e-mail or text message with instructions and a unique pick-up code. Enter your pickup code and the Locker slot with your package will open. Your package will be available for pick-up for three business days after you receive your pickup code.
U.S. Post Office General Delivery
The other, second option is to use the good ol' Post Office. Yup, good ol' USPS. Kevin and Ruth Read, a longtime traveling couple, suggests using the General Delivery service that some post offices offer.
According to the USPS FAQ, this little used option is intended to be a “...a mail service for those without a permanent address, often used as a temporary mailing address.”
This also works for people who don't have an address. Sounds like me.
The package gets sent to a post office where it is held until the recipient picks it up. Mail and packages won't be held for no more than than 30 days, unless requested by sender or addressee and approved by postmaster.
To be sure of timing, check out the official FAQ, but the post office is at least required to hold it for at least 10 days.
To check if a specific post office offers General Delivery, it must be a service listed on the USPS website. I actually highly recommend checking this beforehand since not every post office offers the service. (For instance, the Carmel, Calif. Post Office offers it but the post office in Anaheim, Calif. does not.)
It is also a good idea to check if the post office is open the day the package is scheduled to arrive — there will be no one there to accept the package on a Sunday!
Once that's all done, all is left is addressing the package correctly on Amazon. Per the Reads' instructions:
Here's an example of how it should be addressed...
Kevin Read
PO BOX General Delivery
Mesquite, NV
89024-9999(The add on zip code -9999 must be used for general delivery.)
Once at the post office, travelers will need at least one major form of ID to pick up the package. All there is to it, folks.