I would argue for you to do a more complete routine at your school
gym, but that's not what you asked for...
For something that can be done discreetly, try
exercises such as the goblet squat: take a dumbbell and hold it vertically with two hands, grasping the top "bell". You'll want to keep it a little bit below your chin (I usually have it just away from my sternum) , at a spot where you can feel your mid-section doing some balancing, but you are not putting all the strain on your back (very important!) From here, just do squats! Stick your butt out a little bit to make sure you are using your legs and not your back. Last bit I can think of to help with this exercise is to try and keep the pressure on your heels, not your metatarsals (front of the foot)!
The reason for doing this exercise is that it engages TONS of your muscles and really gets you breathing hard without needing lots of equipment or space. The only hurdle you will have is getting a dumbbell of the right weight, or being inventive and using something around the house
You can do a circuit by performing this squat, switching to crunches or planks (google and youtube can give you good demonstrations), and then to curls or pushups, back around to the squats.
The idea is to build muscle (therefor raising your resting metabolic rate) while getting an aerobic workout in! Hard breathing means a revving metabolism!
Oh, I just remembered, it would be good to use the elliptical before and after doing this, to warm up your muscles before the "lifts" and to loosen them up afterwards.
Basically, best bang for the buck is doing leg
exercises that involve "holding" the
weights you use. The action itself isn't that difficult, but your
body will work hard to deliver all the oxygen to all the muscles you are using!
Hopefully you can use some of this advice, it comes from my experience as an amateur bicycle racer who has always had to deal with a tiny apartment and is too cheap to buy a
gym membership