In reply to Tall Oak:
You can get bars that fit in a doorway that don't require any screwing or drilling. From that you can attach some finger edges too.
If you can go outside you can do pull ups on a tree branch. Kids' playgrounds also provide lots of opportunities, that's where much calisthenics training is done. You can get very portable and adaptable TRX type slings called Monkii Bars
Loads of core stuff can be done on the ground as Alx mentioned above, as can push up type exercises, various squats etc.. Then there's yoga. Tons of yoga stuff on Youtube.
Any specific programme would need to be worked out by you as the right exercises should be determined by your current strength and fitness levels.