View has nothing to do with the actual directory / address, in MVC, controller is the one to deal with this.
Suppose you start with the default template of MVC, the address would be:
http://site.com/CONTROLLER/ACTION/ID
CONTROLLER is the name of the controller class (which under controller directory), ACTION is the method (which return actionresult) within the controller and ID is a string/int that pass as action method parameter.
I think you'd like to have address like:
http://mysite.com/Members/Calendar/admin/
It doesn't really matter where you put the View or controller, but what you should look at is the routing table within the global.asax. Routing mvc tutorial
edit
In the controller, normally you are going to call
return View();
At the end of action. View() is actually an overloaded internal method call of the controlelr class which has 8 different usage. The default without parameter will look for the same view name to the controller. All you need to do in order to reference to different view class other than default, is using: View(IView Class). For example, in your code it might be:
return View(new PROJECT.Members.Calendar.Admin());