Where is Illuminate?

Laravel take the advantage of the autoload features in Composer.

One quick and simple tips:

You can actually find this in composer.lock file. Then find the PSR autoload. For instance, for Laravel/framework:

       {
        "name" : "laravel/framework",
        .......
        .......
        "autoload": {
            "classmap": [
                "src/Illuminate/Queue/IlluminateQueueClosure.php"
            ],
            "files": [
                "src/Illuminate/Foundation/helpers.php",
                "src/Illuminate/Support/helpers.php"
            ],
            "psr-4": {
                "Illuminate\\": "src/Illuminate/"
            }
        }
       }

Since there are a lot of packages in vendor folder, refer the name of the package in the composer.lock. For example, Illuminate is under laravel/framework packages. Then, look for vendor/laravel/framework

Then you know, Illuminate is mapped to vendor/laravel/framework/src/Illuminate

Just to officially answer this question.

The files OP was looking for, along with any other Laravel or package files, are stored in the vendor folder - which you can access from the root Laravel directory.

As @Gavin points out in the comments:

Illuminate is located in /vendor/laravel/framework/src/Illuminate