How to create heirarchical taxonomy menu/list using VIEWS How can I create a view of taxonomy terms for a content type (Story and Page) and display it to a block with parent and child relationship?

What I want is to take a "Taxonomy Term" based on "Content Types".

Example:

Fruits (5)
  - Apple (3)
  - Banana (2)
Vegetables (4)
  - Beans (1)
  - Eggplant (2)
  - Onions (1)


Demo: 
http://worldstogethertravel.com

Menu on right sidebar: (Of Cultural Interest)

This menu is created using taxonomy_menu module not VIEWS.
You can try using Views Tree module..

Project page says


  Views Tree module provides a tree-based style plugin for Views. It is
  equivalent to the tree-based style template from Views 1.
  
  It is based off of the list style. Although it generates a nested
  view, there is still only a single query run for the view making it
  quite performant.


For node count, you can implement same using views.. Check this post Views and node count for taxonomy terms..