Every time I create anew Web site project in VS it creates another folder for a solution file.
\WebSiteName\ \WebSiteName(2)\
In my VS solution explorer it only shows as a Web Site project, no solution file above it. Is there a way I can stop VS creating the solution file when all I want is a web site? Or is it something VS needs?
Yes, it always needs a SLN file. Even if not used. If you open a project file it will create a blank/temp container solution.
The option not to create the solution folder is only available when using New Project. New Website always assumes you want a solution folder and by design is working correctly. If you don't want the folder then use New Project.
Visual Studio however does always require a solution file.