Mostly on the internet.
This is possibly a frame challenge answer.
The point of a hiding place for something is to distinguish between intended and unintended end users of the thing. Actually storing the thing right there is incidental - and for data, completely unnecessary as long as the intended user can directly or indirectly access the internet. We can securely store the data on any hard drive on the planet: put it behind a three-strikes password and a hefty encryption. Even if anybody can identify that your innocuously named, anonymously hosted zip file is, in fact, the secret incriminating documents, they'll never be able to decrypt it.
The only information that needs to be attached to the statue (for whatever story reason it is attached to the statue) is a code which lets the intended recipient know how to look up where to find the data and the password, using information only the intended user is supposed to know.
With so little data that actually needs to be attached to the statue, whatever low tech solution makes sense for the story can do the job. No special technology is required.
Just as an example to explain what I mean:
We could arrange in advance that XXX-ABC-DEFG means start with the B'th word of the A'th chapter of Gulliver’s Travels and transcribe everything for the next C words to get the password. The first E words (no spaces or punctuation) of the D'th chapter of the same book are the back half of various link-shortener links to different hosts of the same encrypted file, and the first G words of the F'th chapter is a duplicate for additional redundancy. XXX is a rural American area code that we picked to signify that the next seven numbers are a code and simultaneously disguise the number as a phone number.