The following snippet can be used to center a given GLFWwindow on any given GLFWmonitor. If there's no need for multi-monitor support, then simply use glfwGetPrimaryMonitor() to get the primary monitor. Thus centering the window by calling centerWindow(window, glfwGetPrimaryMonitor()).

void centerWindow(GLFWwindow *window, GLFWmonitor *monitor)
{
    if (!monitor)
        return;

    const GLFWvidmode *mode = glfwGetVideoMode(monitor);
    if (!mode)
        return;

    int monitorX, monitorY;
    glfwGetMonitorPos(monitor, &monitorX, &monitorY);

    int windowWidth, windowHeight;
    glfwGetWindowSize(window, &windowWidth, &windowHeight);

    glfwSetWindowPos(
        window,
        monitorX + (mode->width - windowWidth) / 2,
        monitorY + (mode->height - windowHeight) / 2);
}

Best Monitor

The "best monitor" is a bit abstract, so let's consider a computer which has two monitors. The "best monitor" could then be defined, as the monitor which the window is mostly on, i.e., if 2/5 of the window is on monitor A and 3/5 of the window is on monitor B, then the "best monitor" would be monitor B.

Any given window can now be centered, on the nearest monitor by doing centerWindow(window, getBestMonitor(window)).

#define MAX(a, b) (((a) < (b)) ? (b) : (a))
#define MIN(a, b) (((b) < (a)) ? (b) : (a))

GLFWmonitor* getBestMonitor(GLFWwindow *window)
{
    int monitorCount;
    GLFWmonitor **monitors = glfwGetMonitors(&monitorCount);

    if (!monitors)
        return NULL;

    int windowX, windowY, windowWidth, windowHeight;
    glfwGetWindowSize(window, &windowWidth, &windowHeight);
    glfwGetWindowPos(window, &windowX, &windowY);

    GLFWmonitor *bestMonitor = NULL;
    int bestArea = 0;

    for (int i = 0; i < monitorCount; ++i)
    {
        GLFWmonitor *monitor = monitors[i];

        int monitorX, monitorY;
        glfwGetMonitorPos(monitor, &monitorX, &monitorY);

        const GLFWvidmode *mode = glfwGetVideoMode(monitor);
        if (!mode)
            continue;

        int areaMinX = MAX(windowX, monitorX);
        int areaMinY = MAX(windowY, monitorY);

        int areaMaxX = MIN(windowX + windowWidth, monitorX + mode->width);
        int areaMaxY = MIN(windowY + windowHeight, monitorY + mode->height);

        int area = (areaMaxX - areaMinX) * (areaMaxY - areaMinY);

        if (area > bestArea)
        {
            bestArea = area;
            bestMonitor = monitor;
        }
    }

    return bestMonitor;
}