I have been told that the best SVN client for Microsoft Windows is Tortoise SVN.
However, when I install it, adds only items to my shell, i.e. the right-click options when I click on folders.
When I try to check out a folder, it tries to create a repository inside the folder I am working on.
I would prefer my repository to be outside of my work. Is this possible?
Creating a repository and using it are two different things.
The "Create repository here" action creates a repository which you can access locally via file://.. syntax or via the svnserve daemon.
The "Checkout" action can be done in any other place. You can either use a local repository, access a repository via http(s) or svnserve.
Ollifant's answer is correct, but as you are about to create your first repository, I just wanted to add that file:// is not at all a recommended method of accessing the repository in a production environment. In fact, according to the svn book it should not really be regarded as an option at all:
Do not be seduced by the simple idea of having all of your users access a repository directly via file:// URLs. Even if the repository is readily available to everyone via a network share, this is a bad idea. It removes any layers of protection between the users and the repository: users can accidentally (or intentionally) corrupt the repository database, it becomes hard to take the repository offline for inspection or upgrade, and it can lead to a mess of file permission problems (see the section called “Supporting Multiple Repository Access Methods”). Note that this is also one of the reasons we warn against accessing repositories via svn+ssh:// URLs—from a security standpoint, it's effectively the same as local users accessing via file://, and it can entail all the same problems if the administrator isn't careful.
svnserve is almost always better then file:// access and it really is almost no additional effort to set up.
If you're trying to run an SVN server of your own that you can then check files into, try VisualSVN. I use it with Tortoise and AnkSVN (all free) and it works great.
Start here: TortoiseSVN Documentation & Subversion Documentation.