Technically, you can out a new project anywhere you like provided you set the correct paths for the API headers and libraries. The easiest way to start would be to duplicate one of the example projects into the same directory (so the existing paths remain valid).
Start by opening one of the example projects to see if you can build and run it. If that works, duplicate the project, rename it and start building your own project. I'd recommend moving it out of the API directory as soon as possible to allow the API to be easily updated (and because the default directory isn't a good path for working documents).
Just update the header paths (C/C++ > General > Additional Include Directories) and library paths (Linker > Input > Additional Dependencies) for a start. There will be a few others, e.g. the path to the resource converter. Use relative paths to make it more portable.
Ralph Wessel BArch
Software Engineer Speckle Systems