I have had the same problem. A nice problem to have. :-)
I shipped a very large box home from Innsbruck, Austria 2 years ago. We went to the post office, bought a box and tape and picked up the necessary paperwork. Then went back to the hotel to pack the box and fill out the paperwork. And back to the post office where they were very helpful and made sure we had the paperwork correctly filled out. If I remember correctly, you just need a general description of the contents (clothes, souvenirs, or whatever) and an estimated value.
I don’t think it cost more than $30 or $40 to ship to the U.S. We filled the box with mostly clothes and used the extra room in our suitcase for all the souvenirs.
Not sure where your hotel is, but this post office is open Saturday 10 -6 (according to Google). Address: Fleischmarkt 19, 1010 Wien, Austria
Good luck!!