There are a minimum of "shoulds" with MODx.
You can install it wherever you like. If you had installed it in htdocs, it would work fine and respond to http://localhost. On a remote site, the equivalent would usually be /public_html.
You could rename your modx-2.0.0-beta directory and MODx could then be accessed by http://localhost/whatever_you_name_it. You’d need to edit the config file, clear the MODx cache and your browser cache/cookies, and reset the paths in some system settings. Since its a new install, it may be easier to just empty the DB, delete the files, and just do a new install.
If the files are in the public_html directory at a remote site,
http://yoursite.com will get you there.
Hope this makes sense.