There is an excellent plugin for Leaflet called Leaflet.Photo.
The plugin was created by Bjørn Sandvik. See the full post: http://blog.thematicmapping.org/2014/08/showing-geotagged-photos-on-leaflet-map.html
The plugin has a number of examples that show usage with image hosting platforms, like Google Photos and Instagram, which have assicaited API's for returning information about the image in question.
I was however keen to host the sollution completely myself, so simply have a folder of images that would populate on the map if they had exif GPS information.
I have created an example available on GitHub:
Simply download the full repo:
Copy the local_file_example folder. Replace the images in the Photos folder with your own photos. Load it onto any php supporting webhost.
Or for more advanced users, the examples below are on: DigitalOcean
And link to the folder with the index.html