A question like this makes me smack my forehead. I am on the other side of security, "security should not interfere with the user experience, unless it is expected or required to prevent the average person doing malicious activity."
Preventing sudo use of vim is just a band aid. As stated earlier, someone can just use:
sudo su -
sudo nano file
sudo my_exectuable_text_editor file
If you are really worried about someone doing something malicious on the box, do not give them sudo (or root password obviously) privileges, period. There is no sliver bullet to prevent malicious activity using sudo and you will only drive yourself crazy by "applying" all the "fixes" to make sure a person can't do anything malicious.
Someone mentioned changing ownership/groups. This is a sticky problem as if the web server is ran as another user, and you change permissions on the file, now all of a sudden your site doesn't work. Well, obviously that wont help you.
You can add yourself to the group the web server runs as, however, if the group doesn't have write access to the files, you would need to perform chmod -R g+w * (or chmod individual files) which may not be what you want and can be a hassle if you have to chmod every file.
Some people even suggested using rvim. Sure, one could just add a line in /etc/sudoers to only allow certain users to sudo rvim, however, it would logically stand that if you had to go that route, it may just be better to implement a web based file manager. This way it is running as the user the web server is running as, thus no file permission issues and you can still have granular control over who edits what files.
My two cents anyways.