I was taught to keep the eyes open, for the above mentioned reason of the ease with which sleep comes when eyes are closed. Also, because in meditation we aren't trying to retreat from anything or shut anything out, but to experience reality.
In my tradition meditation instruction begins with focusing on the out breath, and coming back to that as the object of meditation when the mind wanders. After one practices in this way for a while, the teaching is to bring the soft gaze a bit closer to the body while focusing on both the in and out breathes, and then after this is practiced for a while to lift the gaze a bit and to only focus about 20% of the attention on the breath and the rest on awareness of what's going on (without inner commentary). Then walking meditation (which I've never really liked) the object of meditation is on the movement of the feet and the awareness of the body moving through space.
Then with contemplation I've been taught that after sitting shamatha a while, one can close the eyes and use the contemplative phrase as the object. If the mind wanders, come back to the phrase.
So, that's what I've been taught in my tradition, but I'm still pretty new (only about a year). I guess each tradition will be a bit different. Mine is not specifically Zen, but does incorporate elements of Zen.