Let's say their goal was to simply let us know they were here and possibly share information with us. Perhaps they intended to share their history and cultural encyclopedia. Or something akin to Voyager's cultural payload or a simple time capsule. And let's add the constraint that they wanted us to be able to find it even if we couldn't recognize it for many millions of years.

Thinking out loud:

A monolith somewhere on Earth or on the Moon? With a possible internal 5D optical data storage component?

Would it be buried deep in the Earth? I would guess tectonic activity may make this, as well as any monolith, impractical on Earth.

An object stationed at a LaGrange point? Is this practical given the damage caused by cosmic radiation?

Is there a way to store information that can't be affected by cosmic radiation? Are there other dangers besides impact/radiation/subduction?

Perhaps anchored somewhere deep in the sea?

What would cause us to notice it? I would think they wouldn't want it to have complex machinery and moving parts that would have to continue operating on geologic timescales. Would maintaining high reflectance be feasible over this timescale? If in the sea, maybe the assumption would be that eventually we could map the sea to such a fine resolution such that we would absolutely find some sort of anomalous shaped structure even if not very large?

Curious for any and all input from anyone who has thought much about this or just feels like thinking about it now.