Hi Charlie,
Good. I'd take this approach in this case (I'd try to avoid programming and try to solve as much as possible with geoprocessing aka GP):
Implement a GP service with the upload functionality (10.1) based on the GeoTagged Photos To Points tool. Create a web application that consumes this GP service allowing a user click on a button "Submit photo" - when clicking the button the GP task fires up, user uploads a geotagged photo, and a georeferenced point feature class is created (or a newly created feature class gets appended to an existing feature class with previously added features) behind the scenes on the server side. A feature class has attachments enabled and the source picture is being added as an attachment with the Add Attachments GP tool. The pop-up windows in web application should be used to show the picture attached.
To implement this, you would need ArcGIS Server 10.1 and ArcGIS Desktop 10.1 installation plus learning a bit of geoprocessing and working with GP services (eventually some minor developing with any ArcGIS Web Mapping API). Unfortunately, you cannot do this just with ArcGIS Online..