This is your best friend. It's a pull-up bar that goes in your door frame. Takes literally two seconds to set up, can be removed just as quickly, and allows you to do one of the best workouts you can: a pull-up.
Sure you won't be able to do more than a couple for a while, but you'll get better at them. Start with 1, take a break, do another, take a break and do another. Try for 20-25 a day (not all at once necessarily). Before you know it you'll be cranking out 5 at a time. Then 10. Then 20. It's amazing how quickly you'll progress.
Once you get to that point, shoot for 50 a day total. Then go for 100. Trust me, your body will thank you for it.
Here's an Amazon link if you'd like to buy one.