Assuming your'e standing a long ways away from the monument, your in-camera meter will indeed be mostly useless because the well lit areas are so small compared to the overall darkness of the scene at that distance.
This is where a spot meter comes in handy. Or, you could go up close and meter a swath of light with your in-camera meter (filling the whole viewfinder) and then step back to your preferred viewpoint and apply that setting; keeping in mind where you want the area that you metered to fall on your film's scale of greys.
As for viewing in-camera meters in low light, usually match needles, many cameras have a exposure lock button that will hold the needle in place, and then you can adjust your viewfinder so that you can see the value against a well lit area.
Alternatively, the exposures needed at night aren't apt to change that significantly within a given scenario and you might be able to find a good exposure and stick with it, adjusting when your judgment/experience tells you to.