That is totally up to you, and what goals you want to accomplish. If you work one way for awhile (like cardio first followed by strength training), after six weeks or so you could switch it up and do the other first (like weight training before cardio). Switching things up is a great way to break a plateau.
If the machines are not busy, you can even do it in intervals - ten minutes on the bike, an upper body set, ten minutes on the elliptical, a core workout, ten minutes on the treadmill, a lower body workout. This is actually my favorite, except that all my cardio is done on the bike.
If you have any more questions, please let us know.