Instead of attempting a mega-monument at a single safe location, your species might leave lots of dormant, but durable monuments at lots of places!
I suggest that create landmarks from self-assembling nanomaterials and nanobots, colloquially famous as grey-goo, but actually well within its creators control.
We can already make nanoscale level structures that can take on various shapes, from abstract geometrical shapes to cages for transporting drugs to cancer sites. Some folks at the Technion Institute even succeeded in inscribing the entire Hebrew Bible on a Silicon grain the size of a pinhead in an hour!
Various nanoparticle cages, Image Credit: Nature (2019). DOI: 10.1038/s41586-019-1185-4
A molecular machine walking along a path. See the video on wikimedia commons here.
Your alien civilization, having much more developed science and engineering, and the blessings of the author, would have little difficulty in using these to create artifacts that are several meters or even dozens of miles in size. Moreover, just like real-life cutting-edge materials, these structures can automatically repair themselves from arbitrary damage eons after the creators are gone, probably by incorporating living organisms or nanobots into its structure.
The big advantage of this that once the techniques are developed, they are ridiculous easy and cheap to use at scale (or they can be insanely expensive if you want, perhaps by requiring some rare element). In real life, it would take a materials scientist more than a few hours to make small amounts of such materials in any reasonably stocked chemical laboratory with an autoclave. Your aliens can probably send probes to systems across the galaxy. A probe chooses a nice-looking planet, readies its chemicals and nanobots, and lands on the surface. It finds or bores a deep hole, or even a cave and injects some of its payload, ensuring that a vast underground complex full of carvings would be ready within weeks. It chooses a high cliff and starts spraying, ensuring that permanent statues are now present as long as the cliff lasts. And so on.
Even without FTL, your civilization can leave its marks on widely separated parts of the galaxy, ensuring that at least some of them survive no matter what. Later civilizations can conveniently find them to drive the story.
An even more interesting element is the fact that nanoparticles can change their shape based on things like temperature, the presence of certain chemicals, or even an application of pressure. Proteins in the body are a famous example, and humans have already use this to make molecule sized grippers and cranes.
A moderate dose of handwavium can allow your species to make monuments that only appear when certain rituals are performed. This can conveniently include lighting fires for heat, and making blood or other offerings on a particular spot.
Basically, you get Magic$^{\text{TM}}$ that runs on Science!
This can make for good drama, with a scientifically-minded character seemingly-foolishly insisting on finding a rational explanation in the face of 'obvious' miracles, only to be vindicated (or not) later.
Of course, even with such a highly durable materials you would not want to build your monuments just anywhere. You want to choose planets around stars that will last long, and won't go out with a bang. Red dwarfs are excellent since they have low mass and therefore last really long. They are also well below the Chandrashekhar Limit. The flip side is that many of them are flare stars, and tend to get really bright. Depending on factors like the constitution of your building material, the distance of the planet from the star, and the presence and composition of an atmosphere, it is possible that the radiation may damage the bacteria that repair your structure. Your aliens may solve this problem by choosing stars that don't do this, or planets that are further away from their stars. Or they can miscalculate, so that the monument survives for a long time and then starts disintegrating when their counter-measures fail.
Just make sure you're not near a massive star, or something like a Black Hole or neutron star!