Photographing the Moon is its own subject, separate from golden hour — the Moon is bright enough to shoot deep into the night, but which phase and moment you pick makes a big difference to the result.
Why an exact full moon isn't your best bet
Counterintuitively, a full moon is not the best time for detailed surface shots. Sunlight hits the lunar disk head-on with no side shadows, so craters and mountain ranges look flat. Surface relief shows up best along the terminator — the line between light and shadow — which is present during the waxing and waning quarter phases.
Best phases for different goals
For surface detail, shoot the first or last quarter, when the terminator runs through the middle of the disk. For a dramatic shot of the Moon against a landscape or skyline, catch a thin crescent right after sunset or before sunrise, while the sky still holds some light and foreground detail. For the classic giant orange disk on the horizon, time the moonrise of a full or near-full moon — which you can plan for in advance.
Camera settings
The Moon is lit by direct sunlight, so settings close to daytime shooting work well (the "looney 11" rule): aperture f/8–f/11, shutter speed around 1/125–1/250s, ISO 100–200, a long telephoto lens (300mm or more), and a tripod.
Planning around moonrise
Your city's page on this site shows today's exact moonrise and moonset times along with the current phase and illumination percentage — enough to pick the right evening ahead of time and be in position for moonrise.