You can get leaflet to work in magic mirror quite easily. When you are creating your getDom function take the example from the tutorial as follows:

var mymap = L.map('mapid').setView([51.505, -0.09], 13);
L.tileLayer('https://api.tiles.mapbox.com/v4/{id}/{z}/{x}/{y}.png?access_token={accessToken}', {
            attribution: 'Map data © <a href="http://openstreetmap.org">OpenStreetMap</a> contributors, <a href="http://creativecommons.org/licenses/by-sa/2.0/">CC-BY-SA</a>, Imagery © <a href="http://mapbox.com">Mapbox</a>',
            maxZoom: 18,
            id: 'mapbox.streets',
            accessToken: Your Access token
        }).addTo(this.mymap);

You will also need specify the size of the of the map window in your css file

.Your_Module_Name #mapid {
    height: 500px;
    width: 500px;
}

There is a bit of a bug with some of the map not loading, this can be fixed by listening for the DOM_OBJECTS_CREATED notification like so:

notificationReceived: function (notification, payload, sender) {
        if (notification === "DOM_OBJECTS_CREATED") {
            this.mymap.invalidateSize();
        }
    },

This forces a redraw of the map.