I have this setup in my Gruntfile.js
module.exports = function(grunt) {
    grunt.initConfig({
        less: {
            development: {
                options: {
                    compress: false,
                    yuicompress: false,
                    optimization: 0
                },
                files: {
                    // target.css file: source.less file
                    "assets/css/main.css": "assets/css/main.less"
                },
            } 
        },
        watch: {
            styles: {
                // Which files to watch (all .less files recursively in the less directory)
                files: ['assets/css/*.less', 'assets/less/*.less'],
                tasks: ['less'],
            },
            // Live reload CSS
            css: {
                files: ['assets/css/*.css'],
                options: {
                    nospawn: true,
                    interrupt: false,
                    livereload: true,
                },
            },
        },
    });
    // Watch
    grunt.loadNpmTasks('grunt-contrib-watch');
    // Less Complile
    grunt.loadNpmTasks('grunt-contrib-less');
    grunt.registerTask('default', ['less','watch']);
};
My sylesheet is loaded like this:
<link rel="stylesheet" href="http://project.dev/wp-content/themes/project/style.css">
Whenever I change the css file the I get a 404 error in the browser for this url
http://project.dev/assets/css/main.css?livereload=1392748371895
Which is of course right because the css file lives in:
http://project.dev/wp-content/themes/project/assets/css/main.css
How do I get live reload to get the right URL?
You have to set the base so that Grunt knows where to run the application from. The files the tasks output should be set to reflect the structure Wordpress expects. Its all in the path configuration.
You can achieve a more flexible path structure if you configure it early on Grunt's configuration. Assuming that the Gruntfile.js is in the root of your site (besides the wp-content directory), you could do the following configuration:
grunt.initConfig({
    // configurable paths
    cfg: {
        dist: './wp-content/themes/project'
    },
    // tasks configurations come here...
});
Then on the watch task, you'd set:
livereload: {
    files: ['<%= cfg.dist %>/assets/css/*.css'],
    options: {
        nospawn: true,
        interrupt: false,
        livereload: true
    }
}
The resulting Gruntfile.js would look like:
module.exports = function(grunt) {
    grunt.initConfig({
        // configurable paths
        cfg: {
            dist: './wp-content/themes/project'
        },
        less: {
            development: {
                options: {
                    compress: false,
                    yuicompress: false,
                    optimization: 0
                },
                files: {
                    '<%= cfg.dist %>/assets/css/main.css': '<%= cfg.dist %>/assets/css/main.less'
                }
            } 
        },
        watch: {
            styles: {
                files: ['<%= cfg.dist %>/assets/css/*.less', '<%= cfg.dist %>/assets/less/*.less'],
                tasks: ['less']
            },
            css: {
                files: ['<%= cfg.dist %>/assets/css/*.css'],
                options: {
                    nospawn: true,
                    interrupt: false,
                    livereload: true
                }
            }
        }
    });
    grunt.loadNpmTasks('grunt-contrib-less');
    grunt.loadNpmTasks('grunt-contrib-watch');
    grunt.registerTask('default', ['less','watch']);
};
You'd still have to adjust the above to fit your needs, but the principle is there.
I don't have a setup I can test this on, but I think you need to set the base option:
// Project configuration.
grunt.initConfig({
  connect: {
    server: {
      options: {
        base: 'www-root'
      }
    }
  }
});
See doc here: https://github.com/gruntjs/grunt-contrib-connect/blob/master/README.md#basic-use
Read down through multiple servers if relevant.
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