Nested Image/Video Galleries in Drupal 7
The trick is information architecture. I suggest you use the book module to define the hierarchy. This is an underestimated core module, which works amazingly well and has good integration with Drupal. In a recent site I've architected, all the site navigation was built dynamically using views, book-related contextual filters, and the viewfield module (which allows to put a view inside view). Play with the setup below and enjoy!

Detailed instructions: 


Enable the book module.
Define top galleries as toplevel books, without a parent:


Go to the node editing screen.
Click on the new 'Outline' toplevel tab created by the book module.
Click on the 'Add to book outline' button. This will create a new book.

For each child gallery, select it's parent gallery 


The parent gallery may be one of the toplevel galleries created on the previous steps, or one of the previous child galleries created on this step. 
The child gallery may either be selected on the on the 'Outline' tab (when editing existing nodes) or on the 'Book Outline' vertical tab  displayed below (when creating new nodes).


Create a new view, which will show your toplevel galleies. let's call it "top galleries" 


Open a 'block' display
Make the view field-based.
Add the title field to show the gallery title.
Add a viewfield to show the sub-galleries of this book.
The viewfield will refer to a new view we will create in the next step.
And, most imprtantly, use a filter criteria of Book: Depth (=1)


Create a "gallery-inner" view. 


Open the 'Advanced' setting 
Create a relationship from the node to Book: Parent - the parent book node.
Set a contextual filter to "Content: Nid" taken from the parent book node. 
Now the view show all children of it's parent book.
I haven't tried it but you may also try to add another viewfield here to show the children of those child views recursively, until there is a level with no more children (if it doesn't work, then create anorhter  "gallery-grandchildren" view for the 3rd level. Please report back here and write which way succeeds.
  



Notes: 
- The screenshots were taken from a similar solution, where I've implemented all of the site navigation menus using the book hierarchy defined by the user. So please add an image field to each view where appropriate.