So basically when someone goes to:
I would like to show an Application Page that I have created, without the giant URL. Example of the giant URL :
Is there any way for me to do this?
Of course there is! Go to http://mysite.com/_Layouts/AreaWelcomePage.aspx and change the URL.
Or via the UI:
Site actions > Site Settings > User Interface > Welcome Page and change the URL.
I just tried myself and I see that none of them work. It seems like that the page has to reside in the content database and not just the domain.
Another option is to develop a webpart which automatically redirects to the given application page of your choice.
With either of these 2, you of course can't go to the page and edit it after they are inserted, as they will redirect you ASAP. This can be countered by entering the URL of the set landing page and then add
Hope this helps! :)